Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Tails from the Bulk: Gravitational Decay in AdS$_5$

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that smooth gravitational perturbations of five-dimensional Schwarzschild–AdS black holes decay as a power law rather than 1/log t, and that nonlinear evolutions support the prediction over 4,000 bounces.

desk verdict A careful numerical study that makes a credible case for power-law decay with log-periodic modulation in Schwarzschild-AdS5, but with an exponent that is partly fitted and a late-time approach that is slower than the runs themselves. read the letter →

arxiv 2506.18991 v1 pith:ARS2TJAY submitted 2025-06-23 hep-th gr-qc

John R. V. Crump , Jorge E. Santos This is my paper · ORCID
classification hep-thgr-qc MSC 83C5783C0535B40 PACS 04.70.-s
keywords gravitationalperturbationsSchwarzschild-AdSblackholesquasinormalmodespower-lawdecaystabletrappingnonlinearstabilityAdS/CFTcorrespondenceeikonalapproximation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that smooth, SO(3)-symmetric gravitational perturbations of five-dimensional Schwarzschild–anti-de Sitter (AdS) black holes do not settle down through the widely quoted 1/log t tail. Instead, the late-time decay is a power law, $\|V_4\|^2(v) \propto v^{-2\alpha/C}$, where $\alpha$ measures the exponential falloff of the initial data's angular-momentum spectrum and $C(y_+)$ is a constant set by the black hole radius. The same argument predicts subleading oscillations that are periodic in $\log v$ with period $C$, a fingerprint of the large-angular-momentum (eikonal) sector of the quasinormal-mode spectrum. Fully nonlinear evolutions of two representative black holes, one small and one large, run for over 4,000 AdS wall-crossing times, approach the predicted exponent and show no instability. If correct, the result replaces an inverse-log decay picture with a computable power law and strengthens the case that a sizeable sector of small, smooth perturbations of Schwarzschild-AdS$_5$ is nonlinearly stable.

What carries the argument

The load-bearing object is the quasinormal-mode tail of the boundary energy-density perturbation $V_4$, measured by the norm $\|V_4\|^2(v)$. The argument combines a WKB/eikonal result for the large-$\ell$ decay rates, $\mathrm{Im}\,\omega_\ell \sim -e^{-C\ell+\kappa}$ with $C(y_+)$ given by (2.23), with exponential analyticity of the initial data, $|\tilde V_{4\ell}|\sim e^{-\alpha\ell+\beta}$. Laplace's method converts the mode sum to the power law (2.28), and Poisson summation converts the discrete sum into the log-periodic correction (2.34). The mechanism is that the dominant contribution at time $v$ comes from the modes near the moving peak $\ell_{\max}\sim C^{-1}\log v$, so the late-time tail is a property of the spectrum's slope $\alpha$ and the eikonal constant $C$, not of any single low mode.

What would settle it

Evolve the $y_+=0.5$ initial data to the times where the paper's QNM-decomposition extrapolation claims the power law becomes clean (about $\log v\simeq 42$, or $10^{18}$ crossing times) and compare the log-log slope with $-2\alpha/C\simeq -1.11$; any sustained deviation, or any divergence between the nonlinear run and the QNM extrapolation, would falsify the linear-QNM tail picture. A more accessible test: repeat the evolution with non-analytic (compactly supported) initial data and measure whether the decay becomes $1/\log v$ rather than a power law.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that, within the SO(3)-symmetric sector, the late-time gravitational signal of a Schwarzschild-AdS$_5$ black hole is controlled by a moving peak in angular-momentum space. Because high-$\ell$ quasinormal-mode decay rates degenerate as $\mathrm{Im}\,\omega_\ell \sim -e^{-C\ell+\kappa}$, and because analytic initial data have exponentially decaying mode amplitudes $|\tilde V_{4\ell}|\sim e^{-\alpha\ell+\beta}$, a saddle-point evaluation of the mode sum gives $\|V_4\|^2(v)\propto v^{-2\alpha/C}$, with the peak mode moving as $\ell_{\max}\sim C^{-1}\log v$. Poisson summation adds a universal subleading modulation periodic in $\log v$ with period $C(y_+)$. The paper verifies this behaviour in fully nonlinear evolutions for $y_+=0.5$ and $y_+=1.0$, including the predicted oscillation period and amplitude in the small-black-hole case, and finds that the decay continues for more than 4,000 bounces without sign of turbulent instability. The same power law is seen in the bulk Weyl-curvature norm $\|I_1\|^2$, so the effect is not confined to the boundary quantity $V_4$.

Load-bearing premise

The load-bearing premise is that, once the perturbation is small enough, the late-time dynamics are governed by the linearised Einstein equation and by the fundamental ($n=0$) quasinormal modes, so that nonlinear resonant mode coupling and higher radial overtones do not change the decay exponent even at small amplitude.

Editorial extensions

If this is right

  • The decay is predictable from two inputs — the analytic tail slope $\alpha$ of the initial perturbation and the black-hole-radius-dependent constant $C(y_+)$ — so different initial profiles should yield different but computable power-law exponents.
  • Because the dominant mode number grows as $\ell_{\max}\sim C^{-1}\log v$, observing the true power law requires exponentially long runs for larger black holes; the paper's extrapolation for $y_+=0.5$ indicates the regime only becomes clean after roughly $10^{18}$ crossing times.
  • Higher radial overtones, though long-lived and visible in the spectrum, do not change the exponent because their spectral peaks trail the fundamental-mode peak by a fixed $\ell$ offset; the paper's extrapolations with and without overtones agree.
  • No instability develops within 4,000 bounces in either case, supporting the conjecture that smooth perturbations of Schwarzschild-AdS$_5$ in the SO(3)-symmetric sector are nonlinearly stable, in tension with earlier numerical claims of a $1/\log t$ tail and instability.
  • The same power law appears in the bulk Weyl invariant $\|I_1\|^2$, so the late-time tail is a global spacetime property, not an artefact of the boundary extraction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The exponent's linear dependence on the initial tail slope $\alpha$ is a sharp testable signature: if one ran the same black hole with initial data engineered to have a different $\alpha$, the log-log slope should shift accordingly; failure of that shift would expose the linear-QNM assumption.
  • The mechanism should be generic to asymptotically AdS spacetimes with stable trapping: any setting where high-$\ell$ decay rates vanish exponentially in $\ell$ and initial data are analytic should exhibit a power-law tail with log-periodic modulation, so analogous tails may appear for scalar fields, AdS$_4$, and slowly rotating black holes.
  • The paper's own extrapolation implies the true power law can be invisible for practically inaccessible times (next $10^{18}$ crossing times for $y_+=0.5$), which may explain why prior finite-time numerics reported $1/\log t$ decay; distinguishing the two pictures may require the log-periodic phase signature rather than a single slope measurement.
  • If rough, non-analytic initial data are admitted, the exponential tail $\alpha$ is replaced by a slower decay and the power-law prediction should break down; this is the natural place to look for the weak-turbulence instability conjectured for lower-regularity data.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies gravitational perturbations of five-dimensional Schwarzschild-AdS black holes restricted to an SO(3)-symmetric sector, using ingoing Bondi-Sachs coordinates and fully nonlinear numerical evolutions. From two assumptions—exponentially decaying large-ℓ mode amplitudes for analytic initial data and exponentially decaying quasinormal-mode (QNM) decay rates at large ℓ—the authors derive a late-time power law for the boundary quantity ||V4||^2, with exponent -2α/C and subleading oscillations periodic in log v with period C(y_+). They test this prediction for two horizon sizes, y_+ = 0.5 and y_+ = 1.0, fitting the spectral slope α from the numerical data and reporting agreement with the predicted late-time slope, while finding no sign of instability over 4,000 crossing times (y_+ = 0.5) and 550 crossing times (y_+ = 1.0). The paper also presents a global bulk norm ||I1||^2 as a secondary diagnostic and discusses the slow approach to the asymptotic regime.

Significance. If the main claim holds, the paper would replace the inverse-logarithmic decay picture for smooth SO(3)-symmetric perturbations of Schwarzschild-AdS_5 with a computable power law and would provide evidence for nonlinear stability in this sector, in line with the arguments of Dias et al. The derivation of the power-law functional form, the prediction of the log-periodic oscillations, and the careful treatment of the numerical approach are valuable contributions. The paper is also unusually candid about its limitations, including the finite evolution time, the limited angular resolution, and the reliance on extrapolation for the smaller black hole. The main factor determining the significance is whether the overtone contributions, which the paper itself shows are not negligible, can be properly controlled; as it stands, the quantitative prediction rests on an unverified spectral property of the overtones.

major comments (3)
  1. [Sec. 2.3–2.4 and Fig. 6] The derivation of Eq. (2.28) begins with the assumption that higher overtones n≥1 decay faster than the fundamental n=0 mode and can be ignored. However, Fig. 6 (and Fig. 5, which resolves overtones up to n=7 at ℓ=32) shows that overtone contributions to the V4 spectrum are not small compared with the n=0 mode at high ℓ. The argument in Sec. 2.4 that each overtone's peak sits at a fixed offset from the n=0 peak only shifts the peak; for each overtone n, the contribution to the norm decays as v^{-2α_n/C} with its own tail slope α_n, so the n=0 exponent survives only if α_n ≥ α_0 for every n. No α_n values are measured or reported, and the overtone-inclusive extrapolation is restricted to ℓ≤32 and log v≤42. The central quantitative claim therefore depends on an unverified spectral property of the overtones, and the manuscript should either establish α_n ≥ α_0 or provide a direct measurement of the overtone tail slopes.
  2. [Sec. 3.1, Fig. 7] For y_+ = 0.5, the late-time log-log slope in the actual nonlinear evolution has not converged to the predicted value -2α/C within the 4,000 crossing times shown; the agreement is achieved through a QNM-decomposition extrapolation to log v = 42. Since this extrapolation uses the same linear-QNM and n=0-dominance assumptions that underlie the derivation of (2.28), it cannot independently validate the power-law exponent. The manuscript's statement that the nonlinear evolutions 'support the prediction' should be correspondingly qualified, and the separate status of the extrapolated and directly observed slopes should be made explicit in the main text.
  3. [Secs. 3.1–3.2, Eq. (2.28)] The exponent -2α/C is evaluated using α fitted from the tail of the n=0 spectrum of the same numerical evolution (Fig. 6 at v=8 and v=80; Fig. 9), rather than from an independent characterization of the initial data. As a result, the agreement between the late-time slope and Eq. (2.28) is partially a self-consistency check between two quantities extracted from the same run. This does not invalidate the result, but it weakens the force of the word 'predict' in the abstract and introduction. The authors should state explicitly whether α can be obtained directly from the initial data (for instance from its analyticity domain) and, if so, whether the resulting prediction matches the observed slope.
minor comments (5)
  1. [Sec. 2.4] The estimate for the time v_ℓ at which mode ℓ begins to dominate is stated without derivation; a short explanation of the formula log(v_ℓ) = Cℓ - κ + log(α) - log(e^C - 1) would improve readability.
  2. [Eq. (2.36)] The notation ||I_1||^2 is potentially confusing because I_1 is itself defined as the squared Weyl scalar C_abcd C^abcd; consider using a different symbol or explicitly stating that this is the square of the L^2 norm of I_1 over the hypersurface.
  3. [Figs. 7 and 10] The panels showing the derivative of log||V4||^2 with respect to log v lack explicit axis labels and legends for the shaded prediction regions; please add them for clarity.
  4. [Abstract and Sec. 2.1] The parameter y_+ is used in the abstract and throughout without definition; please define it at first occurrence, for example as the horizon radius in AdS units.
  5. [General] There are several typographical issues, including 'invis given byπy +' in Sec. 3.1 and an incomplete reference entry for [111] (missing year). Please correct these.

Circularity Check

2 steps flagged · score 6.0 of 10

Quantitative decay exponent is a rescaled fit of the same run's spectral slope; the overtone rescue redefines the fit after the original premise fails.

  1. fitted input called prediction [Section 3.1 (Results, y_+ = 0.5), using Eqs. (2.25) and (2.28) of Section 2.3]
    "A straight line fit to the tail of the n=0 spectrum on a log plot for this choice of initial data is shown in Fig. 6. The fitted slope is −α=−0.787. The predicted late time power law exponent is then approximately −2α/C=−1.11."

    The central quantitative prediction (2.28), ||V4||^2 ∝ v^(−2α/C), is 2/C times the slope α that is fitted from the same numerical evolution whose late-time decay is then said to 'approach' the prediction. The saddle-point evaluation makes the time exponent a deterministic function of the spectral slope: once α is measured from the run and C is taken from the QNM formula, the predicted exponent is fixed by construction. The agreement shown in Fig. 7 is therefore a consistency relation between the early-time spectrum and the late-time gradient of the same solution, not an independent verification of the exponent. The same procedure is repeated for y_+ = 1.0 in Sec. 3.2, where the fitted α = 0.38±0.02 directly yields the 'prediction' −2α/C = −2.47±0.13.

  2. other [Section 3.1 (Fig. 6 discussion), with the assumption stated in Section 2.3 and the rescue argument in Section 2.4]
    "Fig. 6 shows the V4 spectrum and overtone spectra at early times and we see that this assumption does not hold. ... A consequence of this is that the slope of the spectrum −α in the power law prediction should be taken from the tail of the n=0 spectrum rather than the full V4 spectrum."

    The power-law derivation was introduced with the premise 'We ignore higher overtones n≥1 for each ℓ as these decay faster than the fundamental n=0 modes.' The paper then reports that the premise fails in the actual data. The rescue is to redefine α as the n=0 tail slope and to assert that the peak of the spectrum is n=0-dominated, but this assertion is backed only by the same QNM decomposition that is used for the extrapolated validation. No overtone spectral slopes α_n are reported, and the argument that overtone peaks sit at fixed offsets only shifts the contributing mode number; whether the n=0 exponent survives depends on unmeasured α_n values. The validation and the assumption thus share the same input.

full rationale

The general functional form — a power law modulated by log(v)-periodic oscillations, replacing the 1/log t picture — is a genuine derivation from QNM exponential degeneracy and analyticity, and the fully nonlinear evolution to 4,000 bounces is independent evidence against the inverse-log decay of [88]. The constant C(y_+) in (2.23) is cited from the authors' prior WKB work [105], but it is a parameter-free analytic formula with stated assumptions and is consistent with the linearized QNM decay rates plotted in Fig. 1, so under the review rules that self-citation is not itself scored as circular. The circularity is partial and quantitative: every quoted 'prediction' of the late-time exponent is obtained by dividing a slope α fitted from the same run by C, so the agreement of the log-log derivative with −2α/C is, to leading order, the solution approaching its own fitted input. The overtone issue compounds this: the clean n=0 assumption is explicitly contradicted by Fig. 6, and the paper preserves the prediction by declaring the n=0 tail to be the correct fit without measuring the overtone slopes that would decide the matter. These points affect the central numerical claim (the precise exponent and its stability significance) while leaving the power-law functional form and the absence of instability in the evolved timescales as independent content; hence a 6 rather than a higher score.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central prediction rests on: (i) the QNM decay-rate asymptotics Im(omega_ell) ~ -exp(-C ell + kappa) with C(y+) from the WKB analysis of [29, 105], cited and self-cited, which the paper partially checks at low ell; (ii) exponential decay of harmonic coefficients for analytic initial data, a standard fact; (iii) the assumption that linearized, fundamental-mode QNM dynamics dominate late times; and (iv) the measured spectral slope alpha, a fitted input. There are no invented entities; the only fitted parameter entering the central exponent is alpha.

free parameters (1)
  • alpha (spectral slope of the V4 tail) = -0.787 (y+ = 0.5); -0.38 +/- 0.02 (y+ = 1.0)
    Obtained by straight-line fits to the tail of the n=0 mode spectrum at early times (Fig. 6, Fig. 9). The predicted power-law exponent -2alpha/C is directly proportional to this fitted value.
assumptions (6)
  • domain assumption For high angular momentum ell, the fundamental QNM decay rates of Schwarzschild-AdS5 obey Im(omega_ell) ~ -exp(-C ell + kappa) with C(y+) from (2.23).
    Taken from [29, 105] (WKB); used in Eq. (2.22)-(2.25). Numerics verify the low-ell rates (Figs. 3-5) but do not test the asymptotic regime directly.
  • standard math Analytic initial data on the sphere have harmonic coefficients decaying at least exponentially: |V4_ell(v0)| <= exp(-alpha ell + beta).
    Standard coefficient decay for analytic functions on [-1,1] in the Chebyshev basis; invoked in Section 2.3 before Eq. (2.26). The value of alpha is measured, not derived.
  • domain assumption At late times the perturbation is small enough that the linearised Einstein equation and the fundamental-mode QNM expansion describe the decay.
    Stated in Section 2.3: 'The behaviour of the remaining small perturbation can be studied by approximating the dynamics using the linearised Einstein equation'. Nonlinear evolutions and the QNM extrapolation support it on the probed timescales.
  • domain assumption Higher radial overtones n>=1 do not change the power-law index because their spectral peaks trail the n=0 peak by a fixed number of modes.
    Discussed in Section 2.4 and Section 3.1; overtone spectra are resolved (Fig. 6) and found not to alter the prediction within the explored timescale.
  • domain assumption The apparent-horizon excision at z=1 with boundary condition (2.6) gives a well-posed numerical Cauchy problem for the causal domain.
    Standard characteristic/Bondi-Sachs treatment; described in Section 2.1, with Newton-Krylov construction of horizon-satisfying initial data in Appendix B.
  • standard math The Poisson summation and saddle-point approximations on the mode sum are valid in the late-time limit (Eq. 2.27-2.33).
    Laplace method and Poisson summation for the exponentially suppressed tail; the truncation to |n|<=1 is justified by gamma-function decay.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tails from the Bulk: Gravitational Decay in AdS$_5$." pith.science (2026). https://pith.science/paper/ARS2TJAY

@misc{pith2026250618991,
  author       = {Pith},
  title        = {Pith review of: Tails from the Bulk: Gravitational Decay in AdS$_5$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ARS2TJAY}},
  note         = {Machine review of arXiv:2506.18991}
}
abstract

We study gravitational perturbations of Schwarzschild-AdS black holes in $d = 5$ and identify a regime of late-time power-law decay for smooth initial data. Based on an analysis of the quasinormal mode spectrum, we predict and characterise this decay behaviour. We perform fully nonlinear numerical evolutions with long integration times that support the prediction and exhibit no signs of instability. Remarkably, the decay is modulated by a universal oscillatory pattern, consistent with subleading corrections from a large-angular-momentum (eikonal) analysis of the quasinormal mode spectrum.

Figures

Figures reproduced from arXiv: 2506.18991 by the authors.

Figure 1
Figure 1. Plots of the log of the quasinormal fundamental mode decay rates log ( [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Plots of log (Im(ωℓ+1)/ Im(ωℓ)) C(y+) −1 for y+ = 0.5 and y+ = 1. WKB analysis shows that this tends to −1 at large ℓ. The rate at which it approaches −1 depends on y+. 2.5 Marching orders and new variables Initial data is specified by choosing A, χ4, U4, and V4 at time v = 0. The apparent horizon condition must be satisfied on the initial slice, so in practice we specify A, U4, and V4 and then find χ4 such that (2.… view at source ↗
Figure 3
Figure 3. Plots of the log of the ℓ = 2, 3, 4, 5 modes of V4 at early times are shown in blue. Fits to a single QNM are shown in orange. The fitted frequencies ω fit l are shown alongside the frequencies ωl of the fundamental n = 0 modes of the linearised equations. QNM behaviour ceases when a mode decays to the point where nonlinear interactions of other modes takes over, seen here for ℓ = 2 after v/y+ ≳ 50 [PITH_FULL_IMAGE… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: (Left) Plot of the ℓ = 11 mode of V4 at early times and a fit to a sum of three QNMs which we identify as the n = 0, 1, 2 overtones. Interference of the n = 0 and n = 1 overtones produces prominent low-frequency beating. (Right) Plot with overlays showing the fitted ov…
Figure 5
Figure 5. Figure 5: (Top left) Plot of the early time evolution of the ℓ = 32 mode of V4 and a fit to a sum of eight QNMs which we identity as the overtones up to n = 7. (Bottom) Plot with overlays showing the overtones. Interference between overtones causes low-frequency beating and larg…
Figure 6
Figure 6. Figure 6: (Left) Plot of the spectrum of each resolvable overtone of V4 at time v = 8. The amplitude of V˜ 4 ℓ is shown in black. A straight line fit to the tail of the n = 0 spectrum with fitted gradient −α = −0.787 is shown in grey. (Right) Plot at time v = 80. The peak of the…
Figure 7
Figure 7. Figure 7: (Top) Plot of log (||V4||2 ) against log(v) for the first 4000 AdS crossing times for y+ = 0.5. The blue curve shows the maximum over each crossing time. Orange dashed straight lines with gradient equal to the predicted power law exponent are shown for comparison. (Bot…
Figure 8
Figure 8. Figure 8: Plot of the decay of ||I1||2 for the first 4000 AdS crossing times for y+ = 0.5, with the exact Schwarzschild-AdS value subtracted. The approach to a straight line at late times suggests a regime of power law decay. 3.2 A large black hole: y+ = 1.0 We choose initial da…
Figure 9
Figure 9. Figure 9: Snapshots of the V4 spectrum for y+ = 1.0 at equally spaced times in log(v). The peak of the spectrum moves to higher ℓ linearly with C(y+) −1 log(v) at late times. A straight line fit to the tail of the spectrum, shown in grey, gives a gradient of approximately −α = −…
Figure 10
Figure 10. Figure 10: (Top) Plot of log (||V4||2 ) against log (v) for y+ = 1.0 for the first 550 AdS crossing times. The maximum over each crossing time is shown in blue. (Bottom) The derivative of the maximum of log (||V4||2 ) over each crossing time with respect to log (v) is shown in d…
Figure 11
Figure 11. Figure 11: Plot of the log of ||I1||2 with the exact Schwarzschild-AdS value subtracted against log (v) for the first 550 crossing times for y+ = 1.0. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Holographic Turbulence and Numerical Estimate of the Fractal Dimension of the Turbulent Horizon

    hep-th 2025-10 conditional novelty 6.0 of 10

    A driven holographic black hole exhibits turbulence whose horizon has fractal dimension D≈2.65 and whose dual fluid energy spectrum scales as k^{−1.79}.

Reference graph

Works this paper leans on

114 extracted references · 16 canonical work pages · cited by 1 Pith paper

  1. [1]

    Stability of a Schwarzschild singularity

    Tullio Regge and John A. Wheeler. “Stability of a Schwarzschild singularity”. In:Phys. Rev.108 (1957), pp. 1063–1069.doi:10.1103/PhysRev.108.1063

    doi:10.1103/physrev.108.1063 1957

  2. [2]

    Stability of the schwarzschild metric

    C. V. Vishveshwara. “Stability of the schwarzschild metric”. In:Phys. Rev. D1 (1970), pp. 2870– 2879.doi:10.1103/PhysRevD.1.2870

    work page doi:10.1103/physrevd.1.2870 1970

  3. [3]

    Effective potential for even parity Regge-Wheeler gravitational perturbation equations

    Frank J. Zerilli. “Effective potential for even parity Regge-Wheeler gravitational perturbation equations”. In:Phys. Rev. Lett.24 (1970), pp. 737–738.doi:10.1103/PhysRevLett.24.737. 21

    doi:10.1103/physrevlett.24.737 1970

  4. [4]

    Nonspherical perturbations of relativistic gravitational collapse. 1. Scalar and gravitational perturbations

    Richard H. Price. “Nonspherical perturbations of relativistic gravitational collapse. 1. Scalar and gravitational perturbations”. In:Phys. Rev. D5 (1972), pp. 2419–2438.doi:10.1103/PhysRevD. 5.2419

    doi:10.1103/physrevd 1972

  5. [5]

    Radiation fields in the schwarzschild background

    J. M. Bardeen and W. H. Press. “Radiation fields in the schwarzschild background”. In:J. Math. Phys.14 (1973), pp. 7–19.doi:10.1063/1.1666175

    doi:10.1063/1.1666175 1973

  6. [6]

    Gravitational perturbations of spherically symmetric systems. I. The exterior prob- lem

    V. Moncrief. “Gravitational perturbations of spherically symmetric systems. I. The exterior prob- lem.” In:Annals Phys.88 (1974), pp. 323–342.doi:10.1016/0003-4916(74)90173-0

    doi:10.1016/0003-4916(74)90173-0 1974

  7. [7]

    Note on the stability of the Schwarzschild metric

    Robert M. Wald. “Note on the stability of the Schwarzschild metric”. In:Journal of Mathematical Physics20.6 (June 1979), pp. 1056–1058.issn: 0022-2488.doi:10 . 1063 / 1 . 524181. eprint: https://pubs.aip.org/aip/jmp/article-pdf/20/6/1056/19001857/1056\_1\_online.pdf. url:https://doi.org/10.1063/1.524181

    doi:10.1063/1.524181 1979

  8. [8]

    The linear stability of the Schwarzschild solution to gravitational perturbations

    Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski. “The linear stability of the Schwarzschild solution to gravitational perturbations”. In:Acta Mat.222.1 (2019), pp. 1–214.doi:10.4310/ acta.2019.v222.n1.a1. arXiv:1601.06467 [gr-qc]

    arXiv 2019

Show all 114 references
  1. [9]

    The non-linear stability of the Schwarzschild family of black holes

    Mihalis Dafermos et al. “The non-linear stability of the Schwarzschild family of black holes”. In: (Apr. 2021). arXiv:2104.08222 [gr-qc]

    2021 arXiv

  2. [10]

    Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

    Sergiu Klainerman and Jeremie Szeftel. “Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations”. In: (Nov. 2017). arXiv:1711.07597 [gr-qc]

    2017 arXiv

  3. [11]

    The global non-linear stability of the Kerr-de Sitter family of black holes

    Peter Hintz and Andr´ as Vasy. “The global non-linear stability of the Kerr-de Sitter family of black holes.” In:Acta Math.220.1 (2018), pp. 1–206.doi:10.4310/ACTA.2018.v220.n1.a1. arXiv:1606.04014 [math.DG]

    2018 arXiv

  4. [12]

    The LargeNlimit of superconformal field theories and supergravity

    Juan Martin Maldacena. “The LargeNlimit of superconformal field theories and supergravity”. In:Adv. Theor. Math. Phys.2 (1998), pp. 231–252.doi:10.4310/ATMP.1998.v2.n2.a1. arXiv: hep-th/9711200

    1998 arXiv

  5. [13]

    Gauge theory correlators from noncritical string theory

    S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov. “Gauge theory correlators from noncritical string theory”. In:Phys. Lett. B428 (1998), pp. 105–114.doi:10 . 1016 / S0370 - 2693(98)00377-3. arXiv:hep-th/9802109

    1998 arXiv

  6. [14]

    Anti de Sitter space and holography

    Edward Witten. “Anti de Sitter space and holography”. In:Adv. Theor. Math. Phys.2 (1998), pp. 253–291.doi:10.4310/ATMP.1998.v2.n2.a2. arXiv:hep-th/9802150

    1998 arXiv

  7. [15]

    Large N field theories, string theory and gravity

    Ofer Aharony et al. “Large N field theories, string theory and gravity”. In:Phys. Rept.323 (2000), pp. 183–386.doi:10.1016/S0370-1573(99)00083-6. arXiv:hep-th/9905111

    2000 arXiv

  8. [16]

    Dynamics of Dimensional Reduction

    Peter G. O. Freund and Mark A. Rubin. “Dynamics of Dimensional Reduction”. In:Phys. Lett. B97 (1980), pp. 233–235.doi:10.1016/0370-2693(80)90590-0

    1980 doi

  9. [17]

    Black holes with a single Killing vector field: black resonators

    ´Oscar J. C. Dias, Jorge E. Santos, and Benson Way. “Black holes with a single Killing vector field: black resonators”. In:JHEP12 (2015), p. 171.doi:10.1007/JHEP12(2015)171. arXiv: 1505.04793 [hep-th]

    2015 arXiv

  10. [18]

    Black resonators and geons in AdS5

    Takaaki Ishii and Keiju Murata. “Black resonators and geons in AdS5”. In:Class. Quant. Grav. 36.12 (2019), p. 125011.doi:10.1088/1361-6382/ab1d76. arXiv:1810.11089 [hep-th]

    2019 arXiv

  11. [19]

    Holographic Superconductors

    Sean A. Hartnoll, Christopher P. Herzog, and Gary T. Horowitz. “Holographic Superconductors”. In:JHEP12 (2008), p. 015.doi:10 . 1088 / 1126 - 6708 / 2008 / 12 / 015. arXiv:0810 . 1563 [hep-th]

    2008

  12. [20]

    A Scalar field condensation instability of rotating anti-de Sitter black holes

    Oscar J. C. Dias et al. “A Scalar field condensation instability of rotating anti-de Sitter black holes”. In:JHEP11 (2010), p. 036.doi:10 . 1007 / JHEP11(2010 ) 036. arXiv:1007 . 3745 [hep-th]

    2010

  13. [21]

    Hairy black holes and solitons in globalAdS 5

    Oscar J. C. Dias et al. “Hairy black holes and solitons in globalAdS 5”. In:JHEP08 (2012), p. 117.doi:10.1007/JHEP08(2012)117. arXiv:1112.4447 [hep-th]

    2012 arXiv

  14. [22]

    A deformed IR: a new IR fixed point for four-dimensional holographic theories

    Gary T. Horowitz, Maciej Kolanowski, and Jorge E. Santos. “A deformed IR: a new IR fixed point for four-dimensional holographic theories”. In:JHEP02 (2023), p. 152.doi:10 . 1007 / JHEP02(2023)152. arXiv:2211.01385 [hep-th]

    2023 arXiv

  15. [23]

    The Black Hole Stability problem

    M. Dafermos. “The Black Hole Stability problem”. In:Talk at the Newton Institute. Available at: http://www-old.newton.ac.uk/webseminars/pg+ws/2006/gmx/1010/dafermos/. University of Cam- bridge, 2006. 22

    2006

  16. [24]

    Dynamic instability of solitons in 4+1 dimensional gravity with negative cosmological constant

    M. Dafermos and G. Holzegel. “Dynamic instability of solitons in 4+1 dimensional gravity with negative cosmological constant”. In:Seminar at DAMTP. Available at: https://www.dpmms.cam .ac.uk/∼md384/ADSinstability.pdf. University of Cambridge, 2006

    2006

  17. [25]

    Christodoulou and S

    D. Christodoulou and S. Klainerman.The Global nonlinear stability of the Minkowski space. Princeton Univ. Press, 1993

    1993

  18. [26]

    Existence and structure of past asymptotically simple solutions of Einstein’s field equations with positive cosmological constant

    H. Friedrich. “Existence and structure of past asymptotically simple solutions of Einstein’s field equations with positive cosmological constant”. In:J. Geom. Phys.3 (1986), pp. 101–117.doi: 10.1016/0393-0440(86)90004-5

    1986 doi

  19. [27]

    On weakly turbulent instability of anti-de Sitter space

    Piotr Bizon and Andrzej Rostworowski. “On weakly turbulent instability of anti-de Sitter space”. In:Phys. Rev. Lett.107 (2011), p. 031102.doi:10 . 1103 / PhysRevLett . 107 . 031102. arXiv: 1104.3702 [gr-qc]

    2011 arXiv

  20. [28]

    Gravitational Turbulent Instability of Anti-de Sitter Space

    Oscar J. C. Dias, Gary T. Horowitz, and Jorge E. Santos. “Gravitational Turbulent Instability of Anti-de Sitter Space”. In:Class. Quant. Grav.29 (2012), p. 194002.doi:10 . 1088 / 0264 - 9381/29/19/194002. arXiv:1109.1825 [hep-th]

    2012 arXiv

  21. [29]

    On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions

    Oscar J. C. Dias et al. “On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions”. In:Class. Quant. Grav.29 (2012), p. 235019.doi:10.1088/0264-9381/29/23/235019. arXiv: 1208.5772 [gr-qc]

    2012 arXiv

  22. [30]

    Scalar Collapse in AdS

    Alex Buchel, Luis Lehner, and Steven L. Liebling. “Scalar Collapse in AdS”. In:Phys. Rev.D86 (2012), p. 123011.doi:10.1103/PhysRevD.86.123011. arXiv:1210.0890 [gr-qc]

    2012 arXiv

  23. [31]

    Boson stars in AdS spacetime

    Alex Buchel, Steven L. Liebling, and Luis Lehner. “Boson stars in AdS spacetime”. In:Phys. Rev.D87.12 (2013), p. 123006.doi:10.1103/PhysRevD.87.123006. arXiv:1304.4166 [gr-qc]

    2013 arXiv

  24. [32]

    Time-Periodic Solutions in an Einstein AdS- Massless-Scalar-Field System

    Maciej Maliborski and Andrzej Rostworowski. “Time-Periodic Solutions in an Einstein AdS- Massless-Scalar-Field System”. In:Phys. Rev. Lett.111 (2013), p. 051102.doi:10.1103/PhysRevLett. 111.051102. arXiv:1303.3186 [gr-qc]

    2013 arXiv

  25. [33]

    Globally regular instability ofAdS 3

    Piotr Bizon and Joanna Jamuna. “Globally regular instability ofAdS 3”. In:Phys. Rev. Lett. 111.4 (2013), p. 041102.doi:10.1103/PhysRevLett.111.041102. arXiv:1306.0317 [gr-qc]

    2013 arXiv

  26. [34]

    Instability of Flat Space Enclosed in a Cavity

    Maciej Maliborski. “Instability of Flat Space Enclosed in a Cavity”. In:Phys. Rev. Lett.109 (2012), p. 221101.doi:10.1103/PhysRevLett.109.221101. arXiv:1208.2934 [gr-qc]

    2012 arXiv

  27. [35]

    A comment on

    Maciej Maliborski and Andrzej Rostworowski. “A comment on ”Boson stars in AdS””. In: (2013). arXiv:1307.2875

    2013 arXiv

  28. [36]

    Critical scalar field collapse in AdS 3: an analytical approach

    R. Baier, S. A. Stricker, and O. Taanila. “Critical scalar field collapse in AdS 3: an analytical approach”. In:Class. Quant. Grav.31 (2014), p. 025007.doi:10.1088/0264-9381/31/2/025007. arXiv:1309.1629 [gr-qc]

    2014 arXiv

  29. [37]

    Three-dimensional Gravity and Instability of AdS 3

    Joanna Jamuna. “Three-dimensional Gravity and Instability of AdS 3”. In:Acta Phys. Polon. B44.12 (2013), pp. 2603–2620.doi:10.5506/APhysPolB.44.2603. arXiv:1311.7409 [gr-qc]

    2013 arXiv

  30. [38]

    Quantum Quench Across a Zero Temperature Holographic Superfluid Transi- tion

    Pallab Basu et al. “Quantum Quench Across a Zero Temperature Holographic Superfluid Transi- tion”. In:JHEP03 (2013), p. 146.doi:10.1007/JHEP03(2013)146. arXiv:1211.7076 [hep-th]

    2013 arXiv

  31. [39]

    Quasinormal modes for Schwarzschild-AdS black holes: exponential convergence to the real axis

    O. Gannot. “Quasinormal modes for Schwarzschild-AdS black holes: exponential convergence to the real axis”. In:ArXiv e-prints(Dec. 2012). arXiv:1212.1907 [math.SP]

    2012 arXiv

  32. [40]

    Scalar field breathers on anti-de Sitter background

    Gyula Fodor, P´ eter Forg´ acs, and Philippe Grandcl´ ement. “Scalar field breathers on anti-de Sitter background”. In:Phys. Rev.D89.6 (2014), p. 065027.doi:10.1103/PhysRevD.89.065027. arXiv: 1312.7562 [hep-th]

    2014 arXiv

  33. [41]

    On the AdS stability problem

    Helmut Friedrich. “On the AdS stability problem”. In:Class. Quant. Grav.31 (2014), p. 105001. doi:10.1088/0264-9381/31/10/105001. arXiv:1401.7172 [gr-qc]

    2014 arXiv

  34. [42]

    Gravitational turbulent instability of AdS 5

    B. Piotr. “Gravitational turbulent instability of AdS 5”. In:Talk at Strings. Available at: http://physics.princeton.edu/strings2014/slides/Bizon.pdf. Princeton University, 2014

    2014

  35. [43]

    What drives AdS spacetime unstable?

    Maciej Maliborski and Andrzej Rostworowski. “What drives AdS spacetime unstable?” In:Phys. Rev.D89.12 (2014), p. 124006.doi:10.1103/PhysRevD.89.124006. arXiv:1403.5434 [gr-qc]

    2014 arXiv

  36. [44]

    Holographic Relaxation of Finite Size Isolated Quantum Systems

    Javier Abajo-Arrastia et al. “Holographic Relaxation of Finite Size Isolated Quantum Systems”. In:JHEP05 (2014), p. 126.doi:10.1007/JHEP05(2014)126. arXiv:1403.2632 [hep-th]. 23

    2014 arXiv

  37. [45]

    Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox

    Venkat Balasubramanian et al. “Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox”. In:Phys. Rev. Lett.113.7 (2014), p. 071601.doi:10.1103/ PhysRevLett.113.071601. arXiv:1403.6471 [hep-th]

    2014 arXiv

  38. [46]

    Comment on Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox?

    Piotr Bizon and Andrzej Rostworowski. “Comment on Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox?” In:Phys. Rev. Lett.115.4 (2015), p. 049101.doi:10.1103/PhysRevLett.115.049101. arXiv:1410.2631 [gr-qc]

    2015 arXiv

  39. [47]

    Reply to Comment on Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox?

    Venkat Balasubramanian et al. “Reply to Comment on Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox?” In:Phys. Rev. Lett.115.4 (2015), p. 049102.doi:10.1103/PhysRevLett.115.049102. arXiv:1506.07907 [gr-qc]

    2015 arXiv

  40. [48]

    Collapse and Revival in Holographic Quenches

    Emilia da Silva et al. “Collapse and Revival in Holographic Quenches”. In:JHEP04 (2015), p. 038.doi:10.1007/JHEP04(2015)038. arXiv:1412.6002 [hep-th]

    2015 arXiv

  41. [49]

    Renormalization group, secular term resummation and AdS (in)stability

    Ben Craps, Oleg Evnin, and Joris Vanhoof. “Renormalization group, secular term resummation and AdS (in)stability”. In:JHEP10 (2014), p. 48.doi:10 . 1007 / JHEP10(2014 ) 048. arXiv: 1407.6273 [gr-qc]

    2014 arXiv

  42. [50]

    A stochasticity threshold in holography and the instability of AdS

    Pallab Basu, Chethan Krishnan, and Ayush Saurabh. “A stochasticity threshold in holography and the instability of AdS”. In:Int. J. Mod. Phys.A30.21 (2015), p. 1550128.doi:10.1142/ S0217751X15501286. arXiv:1408.0624 [hep-th]

    2015 arXiv

  43. [51]

    Stability of AdS in Einstein Gauss Bonnet Gravity

    Nils Deppe et al. “Stability of AdS in Einstein Gauss Bonnet Gravity”. In:Phys. Rev. Lett.114 (2015), p. 071102.doi:10.1103/PhysRevLett.114.071102. arXiv:1410.1869 [hep-th]

    2015 arXiv

  44. [52]

    Position space analysis of the AdS (in)stability problem

    Fotios V. Dimitrakopoulos et al. “Position space analysis of the AdS (in)stability problem”. In: JHEP08 (2015), p. 077.doi:10.1007/JHEP08(2015)077. arXiv:1410.1880 [hep-th]

    2015 arXiv

  45. [53]

    Geons and the Instability of Anti-de Sitter Spacetime

    Gary T. Horowitz and Jorge E. Santos. “Geons and the Instability of Anti-de Sitter Spacetime”. In:Surveys Diff. Geom.20 (2015), pp. 321–335.doi:10.4310/SDG.2015.v20.n1.a13. arXiv: 1408.5906 [gr-qc]

    2015 arXiv

  46. [54]

    Conserved quantities and dual turbulent cascades in anti-de Sitter spacetime

    Alex Buchel et al. “Conserved quantities and dual turbulent cascades in anti-de Sitter spacetime”. In:Phys. Rev.D91.6 (2015), p. 064026.doi:10.1103/PhysRevD.91.064026. arXiv:1412.4761 [gr-qc]

    2015 arXiv

  47. [55]

    Renormalization, averaging, conservation laws and AdS (in)stability

    Ben Craps, Oleg Evnin, and Joris Vanhoof. “Renormalization, averaging, conservation laws and AdS (in)stability”. In:JHEP01 (2015), p. 108.doi:10.1007/JHEP01(2015)108. arXiv:1412. 3249 [gr-qc]

    2015 doi

  48. [56]

    AdS (In)stability: Lessons From The Scalar Field

    Pallab Basu, Chethan Krishnan, and P. N. Bala Subramanian. “AdS (In)stability: Lessons From The Scalar Field”. In:Phys. Lett.B746 (2015), pp. 261–265.doi:10.1016/j.physletb.2015. 05.009. arXiv:1501.07499 [hep-th]

    2015 arXiv

  49. [57]

    Missing top of the AdS resonance structure

    I-Sheng Yang. “Missing top of the AdS resonance structure”. In:Phys. Rev.D91.6 (2015), p. 065011.doi:10.1103/PhysRevD.91.065011. arXiv:1501.00998 [hep-th]

    2015 arXiv

  50. [58]

    Self-gravitating scalar breathers with negative cosmological constant

    Gyula Fodor, Peter Forg´ acs, and Philippe Grandcl´ ement. “Self-gravitating scalar breathers with negative cosmological constant”. In:Phys. Rev.D92.2 (2015), p. 025036.doi:10.1103/PhysRevD. 92.025036. arXiv:1503.07746 [gr-qc]

    2015 arXiv

  51. [59]

    Collapse of massive fields in anti-de Sitter spacetime

    Hirotada Okawa, Jorge C. Lopes, and Vitor Cardoso. “Collapse of massive fields in anti-de Sitter spacetime”. In: (2015). arXiv:1504.05203 [gr-qc]

    2015 arXiv

  52. [60]

    Resonant Dynamics and the Insta- bility of Anti-de Sitter Spacetime

    Piotr Bizon, Maciej Maliborski, and Andrzej Rostworowski. “Resonant Dynamics and the Insta- bility of Anti-de Sitter Spacetime”. In:Phys. Rev. Lett.115.8 (2015), p. 081103.doi:10.1103/ PhysRevLett.115.081103. arXiv:1506.03519 [gr-qc]

    2015 arXiv

  53. [61]

    Conditionally extended validity of perturbation the- ory: Persistence of AdS stability islands

    Fotios Dimitrakopoulos and I-Sheng Yang. “Conditionally extended validity of perturbation the- ory: Persistence of AdS stability islands”. In:Phys. Rev.D92.8 (2015), p. 083013.doi:10.1103/ PhysRevD.92.083013. arXiv:1507.02684 [hep-th]

    2015 arXiv

  54. [62]

    Islands of stability and recurrence times in AdS

    Stephen R. Green et al. “Islands of stability and recurrence times in AdS”. In: (2015). arXiv: 1507.08261 [gr-qc]

    2015 arXiv

  55. [63]

    Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime

    Nils Deppe and Andrew R. Frey. “Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime”. In: (2015). arXiv:1508.02709 [hep-th]

    2015 arXiv

  56. [64]

    Ultraviolet asymptotics and singular dynamics of AdS perturbations

    Ben Craps, Oleg Evnin, and Joris Vanhoof. “Ultraviolet asymptotics and singular dynamics of AdS perturbations”. In: (2015). arXiv:1508.04943 [gr-qc]. 24

    2015 arXiv

  57. [65]

    Ultraviolet asymptotics for quasiperiodic AdS4 perturbations

    Ben Craps et al. “Ultraviolet asymptotics for quasiperiodic AdS4 perturbations”. In: (2015). arXiv:1508.05474 [gr-qc]

    2015 arXiv

  58. [66]

    A Hidden Symmetry of AdS Resonances

    Oleg Evnin and Chethan Krishnan. “A Hidden Symmetry of AdS Resonances”. In:Phys. Rev. D91.12 (2015), p. 126010.doi:10.1103/PhysRevD.91.126010. arXiv:1502.03749 [hep-th]

    2015 arXiv

  59. [67]

    Necessary conditions for an AdS-type instability

    Dhanya S. Menon and Vardarajan Suneeta. “Necessary conditions for an AdS-type instability”. In: (2015). arXiv:1509.00232 [gr-qc]

    2015 arXiv

  60. [68]

    Scalar field critical collapse in 2+1 dimensions

    Joanna Jalmuzna, Carsten Gundlach, and Tadeusz Chmaj. “Scalar field critical collapse in 2+1 dimensions”. In:Phys. Rev.D92.12 (2015), p. 124044.doi:10 . 1103 / PhysRevD . 92 . 124044. arXiv:1510.02592 [gr-qc]

    2015 arXiv

  61. [69]

    AdS perturbations, isometries, selection rules and the Higgs oscillator

    Oleg Evnin and Rongvoram Nivesvivat. “AdS perturbations, isometries, selection rules and the Higgs oscillator”. In:JHEP01 (2016), p. 151.doi:10.1007/JHEP01(2016)151. arXiv:1512. 00349 [hep-th]

    2016 doi

  62. [70]

    Coherent Cascade: Collapsing Solutions in Global AdS

    Ben Freivogel and I-Sheng Yang. “Coherent Cascade: Collapsing Solutions in Global AdS”. In: (2015). arXiv:1512.04383 [hep-th]

    2015 arXiv

  63. [71]

    AdS nonlinear instability: moving beyond spherical symmetry

    O Dias and Jorge E. Santos. “AdS nonlinear instability: moving beyond spherical symmetry”. In:Class. Quant. Grav.33.23 (2016), 23LT01.doi:10.1088/0264-9381/33/23/23LT01. arXiv: 1602.03890 [hep-th]

    2016 arXiv

  64. [72]

    Detailed ultraviolet asymptotics for AdS scalar field per- turbations

    Oleg Evnin and Puttarak Jai-akson. “Detailed ultraviolet asymptotics for AdS scalar field per- turbations”. In:JHEP04 (2016), p. 054.doi:10.1007/JHEP04(2016)054. arXiv:1602.05859 [hep-th]

    2016 arXiv

  65. [73]

    On the stability of anti-de Sitter spacetime

    Nils Deppe. “On the stability of anti-de Sitter spacetime”. In: (2016). arXiv:1606.02712 [gr-qc]

    2016 arXiv

  66. [74]

    Gauge dependence of the AdS instability problem

    Fotios V. Dimitrakopoulos et al. “Gauge dependence of the AdS instability problem”. In:Phys. Rev.D94.12 (2016), p. 124008.doi:10 . 1103 / PhysRevD . 94 . 124008. arXiv:1607 . 08094 [hep-th]

    2016

  67. [75]

    Fast and Slow Coherent Cas- cades in Anti-de Sitter Spacetime

    Fotios V. Dimitrakopoulos, Ben Freivogel, and Juan F. Pedraza. “Fast and Slow Coherent Cas- cades in Anti-de Sitter Spacetime”. In: (2016). arXiv:1612.04758 [hep-th]

    2016 arXiv

  68. [76]

    Comment on

    Andrzej Rostworowski. “Comment on ”AdS nonlinear instability: moving beyond spherical sym- metry” [Class. Quantum Grav. 33 23LT01 (2016)]”. In: (2016). arXiv:1612.00042 [hep-th]

    2016 arXiv

  69. [77]

    Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes

    Hans Bantilan et al. “Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes”. In: (2017). arXiv:1706.04199 [hep-th]

    2017 arXiv

  70. [78]

    Critical collapse of a rotating scalar field in 2 + 1 dimensions

    Joanna Jalmuzna and Carsten Gundlach. “Critical collapse of a rotating scalar field in 2 + 1 dimensions”. In:Phys. Rev.D95.8 (2017), p. 084001.doi:10 . 1103 / PhysRevD . 95 . 084001. arXiv:1702.04601 [gr-qc]

    2017 arXiv

  71. [79]

    Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations

    Andrzej Rostworowski. “Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations”. In: (2017). arXiv:1701.07804 [gr-qc]

    2017 arXiv

  72. [80]

    Gravitational geons in asymptotically anti-de Sitter spacetimes

    Gr´ egoire Martinon et al. “Gravitational geons in asymptotically anti-de Sitter spacetimes”. In: (2017). arXiv:1701.09100 [gr-qc]

    2017 arXiv

  73. [81]

    The Einstein–null dust system in spherical symmetry with an inner mirror: structure of the maximal development and Cauchy stability

    Georgios Moschidis. “The Einstein–null dust system in spherical symmetry with an inner mirror: structure of the maximal development and Cauchy stability”. In: (2017). arXiv:1704 . 08685 [gr-qc]

    2017

  74. [82]

    A proof of the instability of AdS for the Einstein–null dust system with an inner mirror

    Georgios Moschidis. “A proof of the instability of AdS for the Einstein–null dust system with an inner mirror”. In: (2017). arXiv:1704.08681 [gr-qc]

    2017 arXiv

  75. [83]

    AdS nonlinear instability: breaking spherical and axial symmetries

    Oscar J. C. Dias and Jorge E. Santos. “AdS nonlinear instability: breaking spherical and axial symmetries”. In: (2017). arXiv:1705.03065 [hep-th]

    2017 arXiv

  76. [84]

    Collapse and Nonlinear Instability of AdS Space with Angular Momentum

    Matthew W. Choptuik et al. “Collapse and Nonlinear Instability of AdS Space with Angular Momentum”. In:Phys. Rev. Lett.119.19 (2017), p. 191104.doi:10.1103/PhysRevLett.119. 191104. arXiv:1706.06101 [hep-th]

    2017 arXiv

  77. [85]

    Charting Islands of Stability with Mul- tioscillators in anti–de Sitter space

    Matthew Choptuik, Jorge E. Santos, and Benson Way. “Charting Islands of Stability with Mul- tioscillators in anti–de Sitter space”. In:Phys. Rev. Lett.121.2 (2018), p. 021103.doi:10.1103/ PhysRevLett.121.021103. arXiv:1803.02830 [hep-th]

    2018 arXiv

  78. [86]

    Charged and rotating AdS black holes and their CFT duals

    S. W. Hawking and H. S. Reall. “Charged and rotating AdS black holes and their CFT duals”. In: Phys. Rev. D61 (2000), p. 024014.doi:10.1103/PhysRevD.61.024014. arXiv:hep-th/9908109. 25

    2000 arXiv

  79. [87]

    Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes

    Gustav Holzegel and Jacques Smulevici. “Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes”. In:Commun. Pure Appl. Math.66 (2013), pp. 1751–1802.doi:10.1002/cpa.21470. arXiv:1110.6794 [gr-qc]

    2013 arXiv

  80. [88]

    Non-linear instability of slowly rotating Kerr-AdS black holes

    Pau Figueras and Lorenzo Rossi. “Non-linear instability of slowly rotating Kerr-AdS black holes”. In: (Nov. 2023). arXiv:2311.14167 [hep-th]

    2023

  81. [89]

    Quasinormal modes of AdS black holes and the ap- proach to thermal equilibrium

    Gary T. Horowitz and Veronika E. Hubeny. “Quasinormal modes of AdS black holes and the ap- proach to thermal equilibrium”. In:Phys. Rev. D62 (2000), p. 024027.doi:10.1103/PhysRevD. 62.024027. arXiv:hep-th/9909056

    2000 arXiv

  82. [90]

    Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations

    Vitor Cardoso and Jose P. S. Lemos. “Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations”. In:Phys. Rev. D64 (2001), p. 084017. doi:10.1103/PhysRevD.64.084017. arXiv:gr-qc/0105103

    2001 arXiv

  83. [91]

    Low-lying gravitational modes in the scalar sector of the global AdS(4) black hole

    Georgios Michalogiorgakis and Silviu S. Pufu. “Low-lying gravitational modes in the scalar sector of the global AdS(4) black hole”. In:JHEP02 (2007), p. 023.doi:10.1088/1126-6708/2007/ 02/023. arXiv:hep-th/0612065

    2007 arXiv

  84. [92]

    Rodnianski and M

    I. Rodnianski and M. Dafermos.Private communication. Private communication. year

  85. [93]

    Losing forward momentum holographically

    K. Balasubramanian and C. P. Herzog. “Losing forward momentum holographically”. In:Classical and Quantum Gravity31.12 (2014), p. 125010.issn: 1361-6382.doi:10.1088/0264-9381/31/ 12/125010

    2014 doi

  86. [94]

    Gravitational Waves in General Relativity

    H. Bondi. “Gravitational Waves in General Relativity”. In:Nature186.4724 (1960), p. 535.doi: 10.1038/186535a0

    1960 doi

  87. [95]

    Kaluza-Klein holography

    K. Skenderis and M. Taylor. “Kaluza-Klein holography”. In:Journal of High Energy Physics 2006.05 (2006), pp. 057–057.issn: 1029-8479.doi:10.1088/1126-6708/2006/05/057

    2006 doi

  88. [96]

    A Stress Tensor for Anti-de Sitter Gravity

    V. Balasubramanian and P. Kraus. “A Stress Tensor for Anti-de Sitter Gravity”. In:Commu- nications in Mathematical Physics208.2 (1999), pp. 413–428.issn: 1432-0916.doi:10.1007/ s002200050764

    1999

  89. [97]

    The gravitational Hamiltonian, action, entropy and surface terms

    S. W. Hawking and G. T. Horowitz. “The gravitational Hamiltonian, action, entropy and surface terms”. In:Classical and Quantum Gravity13.6 (1996), pp. 1487–1498.issn: 1361-6382.doi: 10.1088/0264-9381/13/6/017

    1996 doi

  90. [98]

    Linear Stability of Schwarzschild-Anti-de Sitter spacetimes I: The system of gravitational perturbations

    O. Graf and G. Holzegel. “Linear Stability of Schwarzschild-Anti-de Sitter spacetimes I: The system of gravitational perturbations”. In: (2024). arXiv:2408.02251 [gr-qc]

    2024 arXiv

  91. [99]

    Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations

    V. Cardoso and J. P. S. Lemos. “Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations”. In:Physical Review D64.8 (2001).issn: 1089- 4918.doi:10.1103/physrevd.64.084017

    2001 doi

  92. [100]

    On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes

    C. M. Warnick. “On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes”. In: Communications in Mathematical Physics333.2 (Sept. 2014), pp. 959–1035.issn: 1432-0916. doi:10.1007/s00220-014-2171-1

    2014 doi

  93. [101]

    Quasinormal frequencies of Schwarzschild black holes in anti–de Sitter spacetimes: A complete study of the overtone asymptotic behavior

    V. Cardoso, R. Konoplya, and J. P. S. Lemos. “Quasinormal frequencies of Schwarzschild black holes in anti–de Sitter spacetimes: A complete study of the overtone asymptotic behavior”. In: Physical Review D68.4 (2003).issn: 1089-4918.doi:10.1103/physrevd.68.044024

    2003 doi

  94. [102]

    Unstable Horizons

    V. E. Hubeny and M. Rangamani. “Unstable Horizons”. In:Journal of High Energy Physics 2002.05 (2002), p. 027.doi:10.1088/1126-6708/2002/05/027

    2002 doi

  95. [103]

    Small black holes in AdS5×S5

    A. Buchel and L. Lehner. “Small black holes in AdS5×S5”. In:Classical and Quantum Gravity 32.14 (2015), p. 145003.doi:10.1088/0264-9381/32/14/145003

    2015 doi

  96. [104]

    Linear Stability of Schwarzschild-Anti-de Sitter spacetimes II: Loga- rithmic decay of solutions to the Teukolsky system

    O. Graf and G. Holzegel. “Linear Stability of Schwarzschild-Anti-de Sitter spacetimes II: Loga- rithmic decay of solutions to the Teukolsky system”. In: (2024). arXiv:2408.02252 [gr-qc]

    2024 arXiv

  97. [105]

    On the nonlinear stability of asymptotically anti-de Sitter solutions

    J. E. Santos et al. “On the nonlinear stability of asymptotically anti-de Sitter solutions”. In: Classical and Quantum Gravity29.23 (2012), p. 235019.issn: 1361-6382.doi:10.1088/0264- 9381/29/23/235019

    2012 doi

  98. [106]

    L. N. Trefethen.Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics, 2000.doi:10.1137/1.9780898719598

    2000 doi

  99. [107]

    Canuto et al.Spectral Methods: Fundamentals in Single Domains

    C. Canuto et al.Spectral Methods: Fundamentals in Single Domains. 1st ed. Scientific Computa- tion. Springer Berlin, Heidelberg, 2006.doi:10.1007/978-3-540-30726-6. 26

    2006 doi

  100. [108]

    Barycentric Lagrange Interpolation

    J. P. Berrut and L. N. Trefethen. “Barycentric Lagrange Interpolation”. In:SIAM Rev.46 (2004), pp. 501–517.doi:10.1137/S0036144502417715

    2004 doi

  101. [109]

    Canuto et al.Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics

    C. Canuto et al.Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. 1st ed. Scientific Computation. Springer Berlin, Heidelberg, 2007.doi:10.1007/978- 3-540-30728-0

    2007 doi

  102. [110]

    Weak turbulence on Schwarzschild-AdS spacetime

    G. Moschidis and C. Kehle. “Weak turbulence on Schwarzschild-AdS spacetime”. In:Spectral Theory and Mathematical Relativity. Erwin Schrodinger International Institute for Mathematics and Physics, 2023.url:https://www.dpmms.cam.ac.uk/ ~rbdt2/NAGR/NAGR_17_Moschidis. pdf

    2023

  103. [111]

    Kehle and G

    C. Kehle and G. Moschidis.In preparation. Private communication. year

  104. [112]

    J. P. Boyd.Chebyshev & Fourier Spectral Methods. Springer Berlin Heidelberg, 1989.doi:10. 1007/978-3-642-83876-7

    1989

  105. [113]

    Jacobian-free Newton–Krylov methods: a survey of approaches and applications

    D.A. Knoll and D.E. Keyes. “Jacobian-free Newton–Krylov methods: a survey of approaches and applications”. In:Journal of Computational Physics193.2 (2004), pp. 357–397.issn: 0021-9991. doi:https://doi.org/10.1016/j.jcp.2003.08.010

    2004 doi

  106. [114]

    GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

    Youcef Saad and Martin H. Schultz. “GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems”. In:SIAM Journal on Scientific and Statistical Comput- ing7.3 (1986), pp. 856–869.doi:10.1137/0907058. 27

    1986 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.