Pith. sign in

REVIEW 4 major objections 5 minor 48 references

High-energy interactions of charged black holes in full general relativity II: Near-extremal merger remnants and universality with the irreducible mass

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · 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 high-energy collisions of equal-mass, equal-charge, nonspinning black holes near the scattering threshold can leave behind near-extremal Kerr-Newman remnants, and that the horizon areal radius, encoded in the…

desk verdict Genuine new results and honest numerics; the Mirr-universality is plausible but the finite-separation b needs a controlled two-separation check. read the letter →

arxiv 2412.01881 v1 pith:HH7KWBMN submitted 2024-12-02 gr-qc hep-phhep-th

M A. M. Smith , Vasileios Paschalidis , Gabriele Bozzola This is my paper · ORCID
classification gr-qchep-phhep-th MSC 83C5783C3583-08 PACS 04.25.D04.70.Bw04.30.-w
keywords chargedblackholesnumericalrelativityscatteringthresholdzoom-whirlorbitsnear-extremalremnantsKerr-Newmanparameterirreduciblemasscosmiccensorship
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 uses full numerical relativity to simulate high-energy, near-threshold collisions of equal-mass, equal-charge, nonspinning black holes, and argues that the merger remnants can be nearly extremal. The most charged binaries studied produce a Kerr-Newman remnant with extremality parameter $\Upsilon_f = 0.97$, and the maximum attainable $\Upsilon_f$ grows with initial charge-to-mass ratio $\lambda$. The paper also reports that thresholds and peak remnant properties become independent of $\lambda$ once impact parameters are normalized by the sum of the initial irreducible masses, i.e., by the horizon areal radius. This matters because it identifies a gauge-invariant length scale that sets the outcome of horizon-scale scattering events, and it tests how close such encounters can push gravity toward cosmic censorship while staying below it.

What carries the argument

The central object is the irreducible mass $M_{\rm irr}$, proportional to the horizon areal radius, used as a normalizing scale for impact parameters. Alongside it, the paper introduces the specific angular momentum $a \equiv J_{\rm ADM}/M_{\rm ADM}$ as an effective impact parameter, and uses the Kerr-Newman extremality parameter $\Upsilon = \sqrt{J^2/M^4 + Q^2/M^2}$ to characterize remnants. Normalizing by $M_{\rm irr}$ collapses charge-dependent curves for thresholds, peak spin, and peak extremality onto universal curves, which is the mechanism that carries the paper's main claim.

What would settle it

Repeat the threshold and peak runs for $\lambda = 0.6$ at more than twice the initial separation so that $b/d \lesssim 2\%$, and check whether $b_*/M_{\rm irr}$, $b_{\rm scat}/M_{\rm irr}$, and the peak $a/M_{\rm irr} = 1.715$ shift by more than the quoted sampling errors; a charge-dependent shift would refute the universality claim.

Watch

Extended reading notes

Core claim

Simulating 51 binaries with initial Lorentz factor $\gamma \simeq 1.52$, impact parameters $1.8 \leq b/M_{\rm ADM} \leq 3.3$, and charge-to-mass ratios $\lambda \in \{0.0, 0.1, 0.4, 0.6\}$, the paper finds merger remnants with Kerr-Newman parameter $\Upsilon_f$ up to $0.97$, exceeding the extremality of uncharged remnants reported in earlier studies. The peak of $\Upsilon_f$ occurs at $a/M_{\rm irr} = 1.715 \pm 0.005$ for all $\lambda$, while the peak dimensionless spin $j_f$ occurs at $b/M_{\rm irr} = 4.585 \pm 0.005$. The immediate-merger and scattering thresholds, $b_*$ and $b_{\rm scat}$, are charge-independent when normalized by $M_{\rm irr}$, as are the corresponding specific angular momenta $a_*/M_{\rm irr}$ and $a_{\rm scat}/M_{\rm irr}$. Charged binaries radiate a smaller fraction of their mass (maximum $31\%$ of the ADM mass) despite stronger electromagnetic emission, and radiate roughly $72\%$ of the total angular momentum regardless of $\lambda$. The paper concludes that the horizon areal radius sets the fundamental length scale for these interactions and that cosmic censorship is respected in every simulation.

Load-bearing premise

The load-bearing premise is that the impact parameter $b$ defined at finite initial separation $d/M_p = 94.85$, where $b/d \approx 5\%$, faithfully represents the asymptotic impact parameter; if the expected $\mathcal{O}(b/d)$ corrections depend on charge, the claimed universality under $M_{\rm irr}$ normalization could dissolve.

Editorial extensions

If this is right

  • Near-threshold charged mergers can produce Kerr-Newman remnants with $\Upsilon_f \geq 0.96$ across all $\lambda$ studied, with the most extremal remnant at $\Upsilon_f = 0.97$, and cosmic censorship is respected.
  • Binaries with larger $\lambda$ radiate less total energy than uncharged ones despite stronger electromagnetic emission; the maximum radiated energy in the study is $31\%$ of the ADM mass for $\lambda = 0$ and $0.1$.
  • The maximum fraction of angular momentum radiated is nearly independent of $\lambda$, at about $72\%$ of the spacetime total angular momentum.
  • Thresholds and peak remnant properties become universal when normalized by $M_{\rm irr}$, so the outcome of horizon-scale scattering is set by the areal radius rather than the ADM mass.
  • An even-polynomial extrapolation of the maximum $\Upsilon_f$ to $\lambda = 1$ gives $0.994$, suggesting that maximally charged binaries at this Lorentz factor would still not form a naked singularity.

Reading between the lines

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

  • A testable extension would be to check whether the universal peak $a/M_{\rm irr} \simeq 1.715$ already appears in charged test-particle orbits around a single Reissner-Nordström or Kerr-Newman black hole; if so, the universality could be understood without full binary dynamics.
  • The monotonic rise of $\Upsilon_f^{\max}$ with $\lambda$ is only fit up to $\lambda = 0.6$; direct simulations at $\lambda > 0.6$ could reveal whether the trend continues, saturates, or turns over before the $\lambda = 1$ prediction.
  • The tradeoff between more electromagnetic and less gravitational emission at fixed normalized impact parameter suggests that, in realistic astrophysical environments with plasma, the observable electromagnetic counterpart might be suppressed relative to the vacuum prediction.
  • The same $M_{\rm irr}$ normalization could be tested against spinning or unequal-mass binaries; if it holds there, the areal radius would act as a universal ruler for near-threshold encounters more broadly.
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

4 major / 5 minor

Summary. This paper presents a numerical-relativity study of high-energy collisions of equal-mass, equal-charge, nonspinning binary black holes with initial Lorentz factor γ≈1.52 and impact parameters near the scattering threshold. The authors vary the charge-to-mass ratio λ∈{0,0.1,0.4,0.6} and compute threshold impact parameters, merger remnant properties (mass, spin, charge, Kerr-Newman parameter Υ_f), and radiated energy and angular momentum. The central claims are that the immediate-merger and scattering thresholds, and the impact parameters that yield maximal remnant spin and maximal Υ_f, become independent of λ when normalized by the sum of the irreducible masses Mirr (or by the areal radius), that the maximum Υ_f increases with λ and reaches 0.97, and that an even-quadratic extrapolation suggests Υ_f^max(λ=1)=0.994, so cosmic censorship is respected.

Significance. The findings are potentially significant: if the Mirr-universality is genuine, the horizon areal radius would be a fundamental scale for near-threshold horizon-scale scattering, and charged collisions could populate near-extremal Kerr-Newman remnants, providing a new avenue for cosmic-censorship tests. The paper also provides useful energetics data (up to 31% radiated energy, ~72% radiated angular momentum) and a benchmark against Sperhake et al. (7.0% vs 6.8% radiated energy). The numerical infrastructure is established (Einstein Toolkit, TwoChargedPunctures, Canuda), and the authors include a convergence study for a challenging λ=0.6 case, with self-convergence demonstrated for EGW and JEMW. However, the headline universality and near-extremal claims rest on assumptions and error estimates that need strengthening before the conclusions can be considered robust.

major comments (4)
  1. [Sec. III A, Eq. (2), Table I] The central universality claim—that b*/Mirr, bscat/Mirr, a*/Mirr, and the peak positions in Tables III–IV are λ-independent—is built on identifying the finite-separation impact parameter b of Eq. (2), with d/Mp=94.85 and b/d≈5%, with the true asymptotic impact parameter. The authors themselves note that the values differ by ~3% from Paper I, where b/d≈1%, and that O(b/d) corrections are expected. The concern is not the overall shift but whether the correction depends on λ: since Mirr decreases by about 10% from λ=0 to λ=0.6, a charge-dependent correction of only a few percent would produce the observed decrease of b*/MADM and bscat/MADM and would mimic universality after dividing by Mirr. A comparison at a second initial separation, or an estimate of the λ-dependence of the finite-separation correction, is required. In addition, a=J_ADM/M_ADM is not an independent diagnostic: with fixed |P| and equal masses, a/Mirr=(|P|/M_ADM)(b/Mirr), so the a/Mirr alignment is essentially the b/Mirr statement rescaled by a mildly λ-dependent factor, not new evidence for the areal-radius scale.
  2. [Sec. III E, Table VII, and Sec. III B] The headline result Υ_f=0.97 and the peak alignments in Tables III–IV rely on remnant properties extracted with QuasiLocalMeasuresEM, yet the convergence study for the challenging λ=0.6, b/MADM=2.70 case shows that Mf, Jf, jf, and Υ_f do not demonstrate self-convergence. At resolution 2h the deviations are +0.18% (Mf), +1.28% (Jf), +0.91% (jf), and +0.66% (Υ_f); at 1.33h they are −0.04%, −0.29%, −0.21%, and −0.15%. These deviations are comparable to the differences used to distinguish Υ_f=0.96 from Υ_f=0.97 and to locate the peak of Υ_f to ±0.005 in a/Mirr. The manuscript states that the lack of self-convergence could arise from surface-integration truncation error, but no test with varied surface-integration resolution is provided. The near-extremal remnant claim and the universality of peak locations require a convergence study at the most extremal parameters, or a demonstration that the non-convergence is confined to the surface integration.
  3. [Sec. III C, Table III, Table IV] The claim in Sec. III C and the abstract that the maximal jf occurs at b/Mirr=4.585±0.005 for all λ is not supported by Table III. For λ=0.6, the table gives b/Mirr|jmax_f = 4.59 with an asymmetric lower error of −0.2, indicating that the next-highest jf value in the downward direction is 0.2 in b/Mirr away; this is far outside the quoted ±0.005 and means the peak is poorly determined for that value of λ. Similarly, Table IV gives a/Mirr|Υmax_f = 1.72+0.01−0.01 for λ=0.6, which is only marginally consistent with the stated universal value 1.715±0.005. The internal inconsistency between the text and the tables weakens the universality statement and should be resolved with a careful reassessment of the peak-location errors.
  4. [Sec. III C, Fig. 6] The extrapolated value Υ_f^max(λ=1)=0.994 is presented as a prediction that a naked singularity would not form for λ=1. This is not a prediction in the usual sense: it is a second-order polynomial fit to the four data points of the same simulations that define Υ_f^max, and the evenness in λ is assumed rather than derived. The error bars δΥ_f^max used in the fit are themselves constructed from local quadratic fits to the same peak data (Appendix D), so the global fit and its extrapolation do not provide an independent test. The statement should be framed as a tentative interpolation formula with a clear caveat, not as a robust cosmic-censorship prediction.
minor comments (5)
  1. [Sec. II A / Table I] The uncharged λ=0.0 case is missing from Table I, even though uncharged runs exist; including it would directly test the universality against the baseline.
  2. [Sec. II B and Appendix B] The sensitivity of J_GW to the lower integration bound (5.3% for ±10Mp, as reported in Appendix B) is not propagated into the quoted Jrad/JADM values or the abstract's "≈72%" claim; state this systematic uncertainty explicitly in the main text.
  3. [Figures] Several figures contain LaTeX rendering artifacts: "uni03BB" in axis labels, "b/M λDM" in Fig. 1, and a repeated "λ=0.6" in the Fig. 5 legend; these should be fixed.
  4. [Sec. II A] The text should explicitly state that for this setup J_ADM = b|P| (for equal masses and opposite momenta), so that the relation between a, b, and P used in Tables I–IV is transparent.
  5. [Sec. II B] The typo "Newman-Penrsose" should be corrected; also define the extraction radius or state that it is the same as in Paper I.

Circularity Check

2 steps flagged · score 2.0 of 10

No significant circularity: central simulation results are self-contained; two peripheral overclaims (a-diagnostic rescaling and polynomial extrapolation labeled a prediction) are minor.

  1. renaming known result [Sec. III A (Table I) and Sec. III C (Fig. 5, Table IV)]
    "An additional “impact parameter-like” diagnostic is listed in Table I: the specific angular momentum a ≡ JADM/MADM. This diagnostic is useful in later scaling of remnant extremality curves. Note that the values of a∗/Mirr and ascat/Mirr are also independent of λ."

    In the initial-data construction, the total ADM angular momentum is J_ADM = |P| b, and the paper itself defines the estimate b = J_ADM/|P|, so a ≡ J_ADM/M_ADM = (|P|/M_ADM) b. Since |P| = 0.57236 is fixed and M_ADM varies by only about 1% across λ, the a/Mirr curves are constant rescalings of the b/Mirr curves. Thus the claimed a/Mirr universality, including the peak value a/Mirr = 1.715 ± 0.005, is not an independent diagnostic but the same b/Mirr pattern expressed in new coordinates. Presenting a as a new 'impact parameter-like' diagnostic that 'improves' the universality re-labels the already-reported b/Mirr result rather than providing independent evidence.

  2. fitted input called prediction [Sec. III C, Fig. 6 and following paragraph]
    "In Fig. 6 we use a second-order polynomial in λ to fit Υ max f . ... Using the best-fit polynomial, we can extrapolate Υ max f to λ = 1.0 and find that Υ max f = 0.994. Therefore, our extrapolation predicts that a naked singularity would not form for λ = 1. We plan to test this tentative prediction in a future work."

    The extrapolated value Υ_max^f(λ=1) = 0.994 is obtained by evaluating the quadratic polynomial fitted to the paper's own four data points at λ = 1.0 (the displayed fit y = 3.55×10^-2 λ^2 + 0.958 gives 0.9935 ≈ 0.994). No independent datum or first-principles constraint enters at λ = 1; the 'prediction' is the fitted curve continued beyond the sampled range. The paper's hedging ('tentative prediction', future test) limits the severity, but labeling a fit evaluation as a prediction of no naked-singularity formation overstates its status.

full rationale

The central claims — near-extremal remnants (Υ_f = 0.97), radiated energy and angular momentum, and the Mirr-universality of threshold and peak impact parameters — are direct outputs of new full-GR simulations with convergence tests and an external check against Sperhake et al. [7] (6.8% vs 7.0% radiated energy, very good agreement). Mirr is computed from initial horizon areas, not fitted to the thresholds, so the observed λ-independence of b*/Mirr and bscat/Mirr is a genuine empirical pattern inferred from the data, not an identity. The finite-separation definition of b (b/d ≈ 5%) is a validity concern: a charge-dependent O(b/d) correction could mimic the Mirr scaling, and the paper itself notes the 3% difference from Paper I; this is a systematic-uncertainty issue, not circularity. Two minor overclaims are flagged rather than full circular steps: (1) the new diagnostic a = J_ADM/M_ADM is, for these initial data, a = (|P|/M_ADM) b with |P| fixed and M_ADM varying by ~1%, so the a/Mirr 'universality' is a rescaled restatement of the b/Mirr result; (2) the extrapolated Υ_max^f(λ=1) = 0.994 is an evaluation of the authors' own quadratic fit, and calling it a 'prediction' overstates its independence, though the paper labels it tentative and plans future tests. Neither issue undermines the independent content of the merger and radiation results.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims depend on standard numerical relativity assumptions and on two hand-chosen or fitted quantities: the radiation integration bounds and the quadratic fit used for the λ = 1 extrapolation. No new physical entities are postulated.

free parameters (2)
  • Polynomial coefficients for Υ_f^max(λ) fit = c2 = 3.55e-2, c0 = 0.958
    Two-parameter quadratic fit to four simulation points (λ = 0, 0.1, 0.4, 0.6) in Fig. 6, used to extrapolate Υ_f^max to λ = 1.
  • Wave extraction integration boundaries = Per-run local minima after junk radiation and noise onset
    Lower and upper time bounds for radiation integrals are hand-selected per simulation (Sec. II B, App. B); moving the lower bound by ±10Mp changes J_rad^GW by 5.3% for the convergence case.
assumptions (4)
  • domain assumption Einstein-Maxwell equations with puncture initial data accurately describe the binary evolution.
    Section II A; all results depend on the numerical solution of these equations.
  • domain assumption The Kerr-Newman formula Υ = sqrt(J^2/M^4 + Q^2/M^2) with quasilocal M, J, Q of the apparent horizon gives the remnant's true extremality parameter.
    Eq. (1) and Sec. II B; assumes the remnant settles to a Kerr-Newman BH described by these quasilocal charges.
  • domain assumption Truncation at ℓ ≤ 6 in the Newman-Penrose mode decomposition and the chosen time-integration bounds capture the radiated energy and angular momentum.
    Sec. II B; validated only for one uncharged case against Sperhake et al. 2009, and the bounds cause up to 5.3% variation in J_rad^GW for the convergence case.
  • ad hoc to paper The maximum Υ_f grows as an even quadratic polynomial in λ, allowing extrapolation to λ = 1.
    Sec. III C, Fig. 6; no derivation, only the qualitative symmetry λ → -λ.

how reviews work

0 comments
Cite this review

Pith. "Pith review of High-energy interactions of charged black holes in full general relativity II: Near-extremal merger remnants and universality with the irreducible mass." pith.science (2026). https://pith.science/paper/HH7KWBMN

@misc{pith2026241201881,
  author       = {Pith},
  title        = {Pith review of: High-energy interactions of charged black holes in full general relativity II: Near-extremal merger remnants and universality with the irreducible mass},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HH7KWBMN}},
  note         = {Machine review of arXiv:2412.01881}
}
abstract

In a previous paper, arXiv:2411.11960 [gr-qc], we initiated a study of high-energy interactions of charged binary black holes near the scattering threshold, focusing on zoom-whirl orbits. In this second paper in our series, we focus on merger remnant properties and energetics with new simulations of equal-mass, equal-charge, nonspinning binary black holes with variable impact parameter. We find near-extremal merger remnants with Kerr-Newman parameter reaching $\Upsilon_f = 0.97$, and observe that the maximum $\Upsilon_f$ increases monotonically with $\lambda$ for a fixed initial Lorentz factor. We find that binaries with larger $\lambda$ radiate less total energy despite having stronger electromagnetic emission. The maximum energy radiated by a binary in our study is $31\%$ of its gravitational mass. Increasing $\lambda$ has little effect on the maximum angular momentum radiated, which was $\approx 72\%$ of the spacetime total angular momentum for each $\lambda$ explored here. Lastly, we provide additional evidence for the universality with the irreducible mass that we discovered in arXiv:2411.11960 [gr-qc]. The black hole horizon areal radius determines a fundamental, gauge-invariant length scale governing BH interactions near the scattering threshold.

Figures

Figures reproduced from arXiv: 2412.01881 by the authors.

Figure 1
Figure 1. FIG. 1. Top panel: remnant dimensionless spin [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Merger remnant dimensionless spin [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Top panel: The remnant mass [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The remnant charge-to-mass ratio [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Top panel: Remnant dimensionless spin [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Fraction of ADM angular momentum radiated with [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Fraction of the ADM mass radiated as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Portion of ADM mass [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Portion of ADM angular momentum [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Top panel: the [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. The absolute value of the imaginary part of the 2 [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 41 canonical work pages

  1. [1]

    impact parameter-like

    from the charge Qf , gravitational mass Mf , and spin an- gular momentum Jf of the remnant as calculated by QuasiLocalMeasuresEM via Eq. A22 of [29]. Note that Qf equals the sum of the initial BH charges to very high accuracy due to charge conservation. The maxi- mum deviation between the sum of the initial charges and the charge of the merger remnant in ...

    work page

  2. [2]

    33 h 0. 2 0 . 3 TABLE VII. The relative difference of the merger remnant properties calculated with resolution factors 2 h and 1 . 33 h from the reported results calculated with resolution facto r h. We list remnant properties mass Mf , spin angular momentum Jf , dimensionless spin jf , and extremality Υ f . ∆ Mf (%) ∆ Jf (%) ∆ jf (%) ∆Υ f (%) 2 h +0. 18 +...

    work page

  3. [3]

    33 h −0. 04 −0. 29 −0. 21 −0. 15 The merger remnant properties do not demonstrate self-convergence. However, the values show minimal vari- ation with resolution. This suggests that either our res- olutions have reached the accuracy possible with these simulations, or that the truncation error from the sur- face integration necessary to compute quasilocal ...

    work page

  4. [4]

    Glampedakis and D

    K. Glampedakis and D. Kennefick, Zoom and whirl: Ec- centric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction, Physical Review D 66, 044002 (2002)

    work page 2002

  5. [5]

    Others, like λ = 0 .4, have been determined with lower precision

    to high pre- cision. Others, like λ = 0 .4, have been determined with lower precision. The error estimate δΥ max f ( λ ) quantifies for the Υ max f – λ best-fit routine these differences, e.g., that the λ = 0 .4 data point should carry slightly less weight than the λ = 0.1 data point. To compute δΥ max f ( λ ) , we repeat the following pro- cess for each λ i...

    work page

  6. [6]

    M. A. M. Smith, V. Paschalidis, and G. Bozzola, High-energy interactions of charged black holes in full gen eral relativity I: Zoom-whirl orbits and universality with the irreducible mass (2024), arXiv:2411.11960 [gr-qc]

    arXiv 2024

  7. [7]

    Bombelli and E

    L. Bombelli and E. Calzetta, Chaos around a black hole, Classical and Quantum Gravity 9, 2573 (1992)

    1992

  8. [8]

    Levin, R

    J. Levin, R. O’Reilly, and E. J. Copeland, Grav- ity waves from homoclinic orbits of compact binaries, Physical Review D 62, 024023 (2000)

    work page 2000

Show all 48 references
  1. [9]

    Pretorius and D

    F. Pretorius and D. Khurana, Black hole mergers and unstable circular orbits, Classical and Quantum Gravity 24, S83 (2007)

    2007

  2. [10]

    Healy, J

    J. Healy, J. Levin, and D. Shoemaker, Zoom-Whirl Orbits in Black Hole Binaries, Physical Review Letters 103, 131101 (2009)

    2009

  3. [11]

    Sperhake, V

    U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hin- derer, and N. Yunes, Cross Section, Final Spin, and Zoom-Whirl Behavior in High-Energy Black-Hole Col- lisions, Physical Review Letters 103, 131102 (2009)

    2009

  4. [12]

    Gold and B

    R. Gold and B. Br¨ ugmann, Radiation from low-momentum zoom-whirl orbits, Classical and Quantum Gravity 27, 084035 (2010)

    2010

  5. [13]

    Gundlach, S

    C. Gundlach, S. Akcay, L. Barack, and A. Nagar, Criti- cal phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case, Physical Review D 86, 084022 (2012) , publisher: Amer- ican Physical Society

    2012

  6. [14]

    Shibata, H

    M. Shibata, H. Okawa, and T. Yamamoto, High-velocity collision of two black holes, Physical Review D 78, 101501 (2008)

    2008

  7. [15]

    Sperhake, E

    U. Sperhake, E. Berti, V. Cardoso, and F. Preto- rius, Universality, Maximum Radiation, and Absorp- tion in High-Energy Collisions of Black Holes with Spin, Physical Review Letters 111, 041101 (2013)

    2013

  8. [16]

    Healy, A

    J. Healy, A. Ciarfella, and C. O. Lousto, The maximum radiated energy and final spin of high speed colli sion (2024), arXiv:2410.20239

    2024 arXiv

  9. [17]

    Cardoso, L

    V. Cardoso, L. Gualtieri, C. Herdeiro, and U. Sperhake, Exploring New Physics Frontiers Through Numerical Relativity, Living Reviews in Relativity 18, 1 (2015)

    2015

  10. [18]

    E. T. Newman, E. Couch, K. Chinna- pared, A. Exton, A. Prakash, and R. Tor- rence, Metric of a Rotating, Charged Mass, Journal of Mathematical Physics 6, 918 (1965)

    1965

  11. [19]

    Zilh˜ ao, V

    M. Zilh˜ ao, V. Cardoso, C. Herdeiro, L. Lehner, and U. Sperhake, Collisions of charged black holes, Physical Review D 85, 124062 (2012)

    2012

  12. [20]

    Bozzola, Does Charge Matter in High-Energy Collisions of Black Holes?, Physical Review Letters 128, 071101 (2022)

    G. Bozzola, Does Charge Matter in High-Energy Collisions of Black Holes?, Physical Review Letters 128, 071101 (2022)

    2022

  13. [21]

    Bozzola and V

    G. Bozzola and V. Paschalidis, Can quasicircular mergers of charged black holes produce extremal black holes?, Physical Review D 108, 064010 (2023)

    2023

  14. [22]

    G. t. Hooft, Graviton dominance in ultra-high-energy scattering, Physics Letters B 198, 61 (1987)

    1987

  15. [23]

    Amati, M

    D. Amati, M. Ciafaloni, and G. Veneziano, Superstring collisions at planckian energies, Physics Letters B 197, 81 (1987)

    1987

  16. [24]

    Banks and W

    T. Banks and W. Fischler, A Model for High Energy Scattering in Quantum Gravity (1999), arXiv:hep-th/9906038

    1999 arXiv

  17. [25]

    M. W. Choptuik and F. Pretorius, Ultrarelativis- tic particle collisions, Physical Review Letters 104, 10.1103/physrevlett.104.111101 (2010)

    2010 doi

  18. [26]

    Rezzolla and K

    L. Rezzolla and K. Takami, Black-hole production from ultrarelativistic collisions, Classical and Quantum Gravity 30, 012001 (2012)

    2012

  19. [27]

    W. E. East and F. Pretorius, Ultrarelativistic black hole formation, Physical Review Letters 110, 101101 (2013) . 14

    2013

  20. [28]

    Sperhake, E

    U. Sperhake, E. Berti, V. Cardoso, and F. Pre- torius, Gravity-dominated unequal-mass black hole collisions, Phys. Rev. D 93, 044012 (2016) , arXiv:1511.08209 [gr-qc]

    2016 arXiv

  21. [29]

    F. J. Dyson, Ch. 12: Gravitational machines, in Inter- stellar Communication , edited by A. Cameron (W. A. Benjamin, Inc., 1963) pp. 115–120

    1963

  22. [30]

    Cardoso, T

    V. Cardoso, T. Ikeda, C. J. Moore, and C.-M. Yoo, Remarks on the maximum lu- minosity, Phys. Rev. D 97, 084013 (2018) , arXiv:1803.03271 [gr-qc]

    2018 arXiv

  23. [31]

    S. R. Brandt, G. Bozzola, C.-H. Cheng, P. Diener, et al. , The Einstein Toolkit (2021)

    2021

  24. [32]

    Goodale, G

    T. Goodale, G. Allen, G. Lanfermann, J. Mass´ o, T. Radke, E. Seidel, and J. Shalf, The Cactus framework and toolkit: Design and applications, in Vector and Parallel Processing – VECPAR’2002, 5th Internat ional Conference, Lecture Notes in Computer Science (Springer, Berlin, 2003)

    2002

  25. [33]

    Bozzola and V

    G. Bozzola and V. Paschalidis, Initial data for gen- eral relativistic simulations of multiple electrically charged black holes with linear and angular momenta, Physical Review D 99, 104044 (2019)

    2019

  26. [34]

    Witek, M

    H. Witek, M. Zilhao, G. Bozzola, M. Elley, G. Fi- carra, T. Ikeda, N. Sanchis-Gual, and H. Silva, Canuda: a public numerical relativity library to probe fund amental physics (2021)

    2021

  27. [35]

    Sperhake, Binary black-hole evolutions of excision and puncture data, Physical Review D 76, 104015 (2007)

    U. Sperhake, Binary black-hole evolutions of excision and puncture data, Physical Review D 76, 104015 (2007)

    2007

  28. [36]

    Zilh˜ ao, H

    M. Zilh˜ ao, H. Witek, and V. Cardoso, Nonlinear interactions between black holes and Proca fields, Classical and Quantum Gravity 32, 234003 (2015)

    2015

  29. [37]

    Schnetter, S

    E. Schnetter, S. H. Hawley, and I. Hawke, Evolutions in 3D numerical relativity using fixed mesh refinement, Classical and Quantum Gravity 21, 1465 (2004)

    2004

  30. [38]

    Thornburg, A fast apparent horizon finder for three- dimensional Cartesian grids in numerical relativity, Classical and Quantum Gravity 21, 743 (2003)

    J. Thornburg, A fast apparent horizon finder for three- dimensional Cartesian grids in numerical relativity, Classical and Quantum Gravity 21, 743 (2003)

    2003

  31. [39]

    Dreyer, B

    O. Dreyer, B. Krishnan, D. Shoemaker, and E. Schnetter, Introduction to isolated horizons in numerical relativity , Physical Review D 67, 024018 (2003)

    2003

  32. [40]

    Bozzola, kuibit: Analyzing Ein- stein Toolkit simulations with Python, Journal of Open Source Software 6, 3099 (2021)

    G. Bozzola, kuibit: Analyzing Ein- stein Toolkit simulations with Python, Journal of Open Source Software 6, 3099 (2021)

    2021

  33. [41]

    Witek, V

    H. Witek, V. Cardoso, C. Herdeiro, A. Nerozzi, U. Sper- hake, and M. Zilh˜ ao, Black holes in a box: Toward the numerical evolution of black holes in AdS space-times, Physical Review D 82, 104037 (2010)

    2010

  34. [42]

    Bozzola and V

    G. Bozzola and V. Paschalidis, Numerical-relativity sim- ulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches, Physical Review D 104, 044004 (2021)

    2021

  35. [43]

    N. T. Bishop and L. Rezzolla, Extraction of Gravitational Waves in Numerical Relativ- ity, Living Reviews in Relativity 19, 2 (2016) , arXiv:1606.02532 [gr-qc]

    2016 arXiv

  36. [44]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haber- land, T. Reddy, D. Cournapeau, E. Burovski, P. Pe- terson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, I. Po- lat, Y....

    2020

  37. [45]

    M. A. M. Smith, V. Paschalidis, and G. Bozzola, In preparation (2024)

    2024

  38. [46]

    C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gom- mers, P. Virtanen, D. Cournapeau, E. Wieser, J. Tay- lor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del R ´ ıo, M. Wiebe, P. Peterson, P. G´ erard-Marchant, K. She...

    2020

  39. [47]

    HDF5 for Python , http://www.h5py.org/

  40. [48]

    J. D. Hunter, Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering 9, 90 (2007) , con- ference Name: Computing in Science & Engineering. 15 TABLE X. Initial data parameters for the simulations in this work. All binaries have initial linear momentum |P | = ...

    2007

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.