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Black hole collisions, instabilities, and cosmic censorship violation at large D

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Pith's one-line read Colliding black holes in higher dimensions may end in a naked singularity.

desk verdict New angular-momentum radiation formula and quantitative black-bar/black-string match are solid, but the finite-D cosmic censorship claim is weaker than the paper's own 'no plausible alternative' rhetoric. read the letter →

arxiv 1908.03424 v2 pith:4CYDKUEK submitted 2019-08-09 hep-th gr-qc

Tomas Andrade , Roberto Emparan , David Licht , Raimon Luna This is my paper · ORCID
classification hep-thgr-qc MSC 83C5783C7583C35
keywords cosmiccensorshiplarge-DeffectivetheoryblackholecollisionsbarsGregory-Laflammeinstabilityultraspinningholesgravitationalradiationhigher-dimensionalgravity
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 argues that when two black holes with high total angular momentum collide in spacetime dimension D, the merged object can develop a naked singularity, violating cosmic censorship. Using an effective theory valid at large D, the authors show that such collisions pass through a long-lived rotating black bar, and that the bar is unstable in the same way a black string is: it pinches at its middle, with curvature growing without bound in finite time. At finite D, gravitational radiation tries to spin the bar down, but the paper estimates the spin-down to be so slow that it cannot quench the pinch for D at least around 8, and possibly down to D=6. The same instability drives ultraspinning black holes to fragment into smaller black holes, often through transient rings or multi-pronged horizons. If correct, the result means that higher-dimensional general relativity admits processes that end in a naked singularity, resolved only by a tiny Planck-scale evaporation of the neck.

What carries the argument

The engine of the argument is the large-D effective theory, in which a black hole is a gaussian blob of mass density m(t,x) and momentum p_i(t,x) living on a black brane and obeying simple diffusion-like equations. Within that theory, the black bar is the explicit stationary solution (2.21)-(2.22): a rigidly rotating, oblong gaussian whose longitudinal length grows as 1/$\Omega$, so longer bars rotate more slowly. Its leading instability is shown to have a growth rate matching the black-string formula W approximately (($\sqrt$(3))/4)(J/M) - 1. For the finite-D radiation estimate, the load-bearing identity is dE/dt = $\Omega$ dJ/dt, derived from a new D-dimensional quadrupole formula for angular momentum; together with the factorial suppression of the energy rate, it yields a radiative spin-down time of order D^D in units of the instability time, which is order one.

What would settle it

Run a full numerical relativity simulation of a head-on, high-spin black hole collision in D=8, and in D=6 and 7, with total J/M above the bar-instability threshold. The paper predicts the bar pinches to a naked singularity; observing instead that the bar radiates angular momentum and settles to a stable Myers-Perry black hole would falsify the central claim. More narrowly, measuring the angular-momentum radiation of a rotating black bar at D=6 and checking the new quadrupole formula (B.45) would test the key input.

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Extended reading notes

Core claim

The central claim is that a collision of two spinning black holes with sufficient total angular momentum does not simply merge and settle into a stationary black hole. Instead, the merged horizon spends many rotation cycles as a nearly stationary, elongated bar, whose deformation grows at a rate that matches the Gregory-Laflamme instability of black strings. Because the bar can be arbitrarily long and the space has no compact direction to confine it, the pinch at the center is not halted, and the horizon reaches a singularity in finite time. The authors compute gravitational radiation from the bar in any D using a quadrupole formula, prove the general relation dE/dt = $\Omega$ dJ/dt, and find the spin-down time grows factorially with D while the instability time is order one; therefore, for large enough D (most likely D greater than or similar to 8), the bar fragments before radiation can save cosmic censorship. They also show that unstable ultraspinning Myers-Perry black holes generically evolve by breaking off smaller black holes, with transient black rings for axisymmetric perturbations and multi-pronged arms for higher non-axisymmetric modes.

Load-bearing premise

Everything at finite D rests on the assumption that the quadrupole radiation formula for a slowly moving, weakly gravitating ellipsoid correctly describes the spin-down of a strong-field black-hole horizon, including the relation dE/dt = $\Omega$ dJ/dt and the unspecified order-one factor c; if radiation is faster than estimated, the pinch may be quenched, especially near D=6.

Editorial extensions

If this is right

  • For any D greater than or similar to 8 with enough total angular momentum, the endpoint of a two-black-hole merger is a naked singularity, so cosmic censorship fails in higher-dimensional general relativity.
  • Just before the singularity, the horizon forms a Planck-scale neck; if quantum gravity evaporates it like a hot droplet, the long-term outcome is two outgoing black holes whose momenta differ from the initial ones only by Planck-suppressed uncertainties.
  • Ultraspinning black holes at large D die by fragmentation: they shed excess spin by breaking off smaller black holes, rather than by radiating it away.
  • The radiative relation dE/dt = Omega dJ/dt holds for rigidly rotating emitters in all dimensions, so the spin-down of any such bar is fixed once its energy radiation is known.
  • The black-bar instability is quantitatively the Gregory-Laflamme instability of a black string segment, which lets one predict bar break-up times from string data.

Reading between the lines

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

  • The paper does not commit to a precise lower critical dimension; if the order-one coefficient c in its radiation estimate is favorable, the same violation could occur down to D=6, a claim that existing finite-dimension numerical codes can test directly.
  • The same bar-pinch mechanism may apply to other high-energy processes, such as black hole formation from grazing ultrarelativistic particle collisions, whenever the merged horizon is sufficiently elongated and rapidly spinning.
  • The new D-dimensional angular-momentum quadrupole formula provides a benchmark: full nonlinear simulations of bar-mode instabilities at D=6 and D=7 could measure dJ/dt and compare with the formula, sharpening the estimate of the critical dimension for cosmic censorship violation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript uses the large-D effective theory of black holes to simulate, in 2+1 effective dimensions, collisions of spinning black holes and the non-linear evolution of ultraspinning Myers-Perry black holes. It identifies rotating black bars as long-lived intermediate states in mergers with sufficiently high angular momentum per unit mass, shows that the instability of these bars tracks the Gregory-Laflamme instability of black strings (Section 5.2), and uses this to argue for pinch-off towards a naked singularity. To connect to finite D, the authors compute the quadrupolar gravitational-radiation spin-down of a rotating bar (Section 6 and Appendix B), including a new derivation of the angular-momentum radiation formula in even D, and compare the radiative time scale with the Gregory-Laflamme instability time. They conclude that for sufficiently large D, and 'very likely for D ≳ 8', radiation is too slow to quench the instability, so cosmic censorship is violated; additional simulations show transient black rings and multi-pronged horizons in ultraspinning black hole evolutions. The paper is clearly written and the numerical evidence is presented carefully.

Significance. The large-D effective approach converts a hard time-dependent problem into tractable partial differential equations, and the paper substantially strengthens the case that higher-dimensional black hole collisions and instabilities can have cosmic-censorship-violating endpoints. The quantitative match between measured bar growth rates and the black-string formula (Figure 15), the demonstration of intermediate bar formation with excellent agreement to analytic profiles (Figure 8), and the first derivation of the quadrupolar angular-momentum emission formula in D dimensions (Appendix B.3) are valuable contributions. The work also makes falsifiable predictions for finite-D numerical relativity, in particular a critical spin above which fragmentation beats radiation and a critical dimension above which the bar instability dominates. However, the finite-D extrapolation is the weakest link; the paper itself acknowledges several hurdles, and the D ≈ 8 claim is not yet established by the presented estimates.

major comments (3)
  1. [Sec. 6.2–6.3, Eqs. (6.21), (6.29)] The comparison of time scales uses the linear Gregory-Laflamme growth time τ_inst, but Section 6.2 states that in black-string simulations the time to form a large pinch can be 'significantly larger than τ_inst, possibly even two orders of magnitude larger'. This matters numerically: from (6.21) and (6.29), with the common factor (8GM/Ω^{D−4})^{1/(D−3)} cancelled, τ_rad/τ_inst = D Γ((D−1)/2)^2/(2π c), which at D=8 is about 14/c. A nonlinear pinch delay of even 10 τ_inst, or c of order a few, therefore reverses the race at D=8, allowing spin-down to quench the instability. The statement in Section 3.4.1 that centrifugal repulsion 'will accelerate the pinching faster' is not quantified, and the observed faster pinch in the effective-theory simulations cannot by itself settle the finite-D competition because those simulations contain no gravitational radiation. The finite-D conclusion for D ≈ 8 should be softened to an extrapolation unless a quantitative bound on the nonlinear pinch time for black bars is provided.
  2. [App. B.3, Eq. (B.19), Sec. 6.3] The angular-momentum radiation rate (B.45) is derived using the retarded Green's function (B.19), which the authors state holds 'as long as D is even'. Nevertheless, the spin-down time (6.21) is used for all D ≳ 8 and in the 'possibly down to D=6' discussion, including odd D=7. No odd-D derivation or interpolation argument is given. The finite-D comparison should be explicitly restricted to even D, or an odd-D treatment should be supplied, before the D=7 statement can be made.
  3. [Sec. 6.1, Eq. (6.11), Sec. 6.3] The central spin-down estimate contains an undetermined O(1) coefficient c from Eq. (6.11), and Section 6.3 acknowledges that the exponent in 2^D may easily be modified. With the printed formulas, at D=8 one has τ_rad > τ_inst only for c ≲ 14, and at D=7 only for c ≲ 4.5, so the abstract's 'very likely for D ≳ 8' requires c to be near the lower end of O(1) and also requires the nonlinear pinch delay to be absent. The sentence in Section 6.3 claiming that the prefactor comparison holds 'unless c>9' appears inconsistent with the ratio following from (6.21) and (6.29) and should be rechecked. A sensitivity analysis over c and over the nonlinear-delay factor is needed; absent that, the robust statement is only 'for sufficiently large D'.
minor comments (4)
  1. [Fig. 6 caption] The caption says 'The dashed and continuous lines correspond to stationary MP black holes and black bars' but does not identify which line type refers to which solution; please make this explicit.
  2. [Fig. 8 caption] The word 'analityc' should be 'analytic'.
  3. [Section 6, first paragraph] The terms 'death by fragmentation' and 'death by radiation' are used without definition; please define them at first use, since they carry the interpretation of the two competing channels.
  4. [Appendix B.1 and B.2] The quadrupole calculation models the black bar as a rigidly rotating ellipsoid with constant mass density, but the conditions under which this weak-field, slow-motion approximation applies to a strong-field black hole horizon are never stated; a sentence making this limitation explicit would help readers calibrate the estimate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the finite-D race between radiative spin-down and GL-type pinch is a genuine comparison with external benchmarks, not a quantity put in by construction.

full rationale

The central derivation chain is not circular. The collision and bar evolutions are solutions of the large-D effective equations previously derived in [2,12] by the same group, but the paper does not ask the reader to accept the CC-violation claim on the strength of that citation alone: the bar's GL-type instability is cross-checked against the known Gregory-Laflamme instability and its blackfold description [7,15], and against external finite-D numerical simulations [8,26,27]. The spin-down estimate in Sec. 6 and App. B is an actual calculation: the energy loss uses the D-dimensional quadrupole formula of [9], and the angular-momentum rate is derived from first principles in App. B.3, leading to dE/dt = Omega dJ/dt (Eq. 6.13). Applying it to black bars is an explicitly stated model (rotating ellipsoid, App. B.1), not a renamed input. The only unknown coefficient c in Eq. (6.21) is openly identified as an O(1) uncertainty, including possible corrections to the 2^D exponent, and is not fitted from the claimed outcome. The conclusion tau_inst << tau_rad for large D follows from comparing Eq. (6.21) with Eq. (6.29), two independent estimates, and the paper explicitly flags the weak links: the large-D theory cannot itself exhibit a naked pinch (Sec. 3.4.1), the nonlinear pinch time may be up to two orders of magnitude larger than tau_inst (Sec. 6.2), and the minimum dimension D~6-8 is uncertain (Secs. 6.3, 7). These are correctness limitations, not circular reductions. Self-citations to [2,12,14,15] supply the framework and benchmark formulas, but the load-bearing comparisons also involve external results, so no step reduces to its own input by construction.

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

The paper introduces no new particles or forces. Its finite-D conclusion leans on one undetermined order-one constant c, the quadrupole model for black-bar radiation, the black-string analogy for the instability, and the assumption that the large-D effective theory remains representative at finite D. These are the reader's main epistemic burdens.

free parameters (1)
  • c = Undetermined order-one constant; must be small enough (roughly below 9 to 30 depending on D) for the D around 8…
    Introduced in Eq. (6.11) to absorb O(1) uncertainties in the maximum radiation rate and the exponent in 2^D. The robustness of the D >= 8 claim depends on c not being large.
assumptions (6)
  • domain assumption The large-D effective equations (2.1)-(2.2) capture the dynamics of localized black holes over long times.
    Central tool, derived in [12,2], but its validity for nonlinear mergers relies on subleading 1/D corrections being small, which is not proven in this paper.
  • domain assumption The post-merger elongated horizon behaves as a stationary black bar, so its instability rate follows from the black-string analogy (5.5).
    Numerical agreement in Section 5.2 supports this, but only near threshold and for a limited parameter range.
  • domain assumption The D-dimensional quadrupole formula applies to a black bar modeled as a rigidly rotating ellipsoid.
    Appendix B models a strong-field black hole horizon as a slowly moving ellipsoidal source; no error bound is given for this approximation.
  • domain assumption Black string and black bar Gregory-Laflamme instabilities end in a naked singularity rather than settling to a stable non-uniform configuration.
    Based on finite-D simulations [8,26,27]; for bars there is no Kaluza-Klein box, so the analogy is plausible but not directly demonstrated.
  • domain assumption Radiative spin-down proceeds quasistatically, so the first law and dE/dt = Omega dJ/dt hold during emission.
    Assumed in Section 6.1, Eq. (6.15); the authors note this minimizes entropy production, but it is a nontrivial assumption about the evolution.
  • standard math The angular momentum radiation formula in Appendix B.3 follows from standard transverse-traceless decomposition and stress-energy conservation.
    The derivation appears self-contained and uses standard weak-field gravity manipulations; we found no gap in the algebra.

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Cite this review

Pith. "Pith review of Black hole collisions, instabilities, and cosmic censorship violation at large D." pith.science (2026). https://pith.science/paper/4CYDKUEK

@misc{pith2026190803424,
  author       = {Pith},
  title        = {Pith review of: Black hole collisions, instabilities, and cosmic censorship violation at large D},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4CYDKUEK}},
  note         = {Machine review of arXiv:1908.03424}
}
abstract

We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evidence that they lead to violations of cosmic censorship. The post-merger evolution of the collision of two black holes with total angular momentum above a certain value is governed by the properties of a resonance-like intermediate state: a long-lived, rotating black bar, which pinches off towards a naked singularity due to an instability akin to that of black strings. We compute the radiative loss of spin for a rotating bar using the quadrupole formula at finite D, and argue that at large enough D ---very likely for $D\gtrsim 8$, but possibly down to D=6--- the spin-down is too inefficient to quench this instability. We also study the instabilities of ultraspinning black holes by solving numerically the time evolution of axisymmetric and non-axisymmetric perturbations. We demonstrate the development of transient black rings in the former case, and of multi-pronged horizons in the latter, which then proceed to pinch and, arguably, fragment into smaller black holes.

Figures

Figures reproduced from arXiv: 1908.03424 by the authors.

Figure 1
Figure 1. Two spinning black holes collide and form a rotating black bar, which then breaks up into two outgoing black holes different than the initial ones (the figures are high-contrast density plots of the mass density obtained from the numerical simulation of a collision in the large-D effective theory). The purpose of the present article is twofold: first, to provide a more detailed analysis of black hole collisions usin… view at source ↗
Figure 2
Figure 2. Late-time horizon shape of unstable ultraspinning Myers-Perry black holes when per￾turbed with a tripolar and a quadrupolar mode, and then evolved with the large-D effective theory. Further evolution of the black hole suggests that the arms pinch, violating CC through ‘death by fragmentation’ [5]. The quadrupolar ‘star’ and its evolution to singular pinches has been recently observed in numerical simulations in D = … view at source ↗
Figure 3
Figure 3. Phase diagram of MP black holes (blue line) and black bars (black line). Red dots indicate the presence of non-axisymmetric marginal modes. Black circles indicate axisymmetric marginal modes of MP black holes. Observe that marginal modes of MP black holes and black bars appear at the same values of Ω but different J/M. (Reproduced from [2]) theory magnitudes in section 2.2, as M = Ωn+1 16πGr n+2 + n + 3 2πm0 M , (2.… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Growth rates W of unstable modes of MP black holes at D → ∞, as a function of the spin per unit mass J/M of the black hole (as calculated in [21, 2]). Higher non-axisymmetric modes (‘mφ-poles’) become successively dominant as the spin grows, and generically overwhelm t…
Figure 5
Figure 5. Figure 5: Initial data for u = 1, b = 2.5, x0 = 3, and a = 0 (left) and a = 0.5, σ = 1 (right). Here we have chosen units m0 = 1. 3.3 Black hole collision Having set up the initial conditions as described above, we follow the evolution of the system by numerically solving (2.1),…
Figure 6
Figure 6. Figure 6: Final states of collisions for varying impact parameter, initial velocities and spins. The dashed and continuous lines correspond to stationary MP black holes and black bars. The left plot is superimposed on the phase diagram of figure 3. The right plot shows the (squa…
Figure 7
Figure 7. Figure 7: Time evolution of the maximum of the energy density mmax and its value at the origin m(0,0). After a short period, these two values become equal, signaling rigid rotation. At late times, their values begin to differ, as a consequence of the break up of the bar. We extr…
Figure 8
Figure 8. Figure 8: Values of the profiles at t ≈ 22 along the principal axes, in blue and yellow. The data points correspond to the numerical data, while the solid lines show the analityc profiles in (2.21), (2.22). The value of Ω is obtained from our initial data, while mmax is extracte…
Figure 9
Figure 9. Figure 9: Intermediate states of the evolution of the MP black hole with a = 3, after perturbations with mφ = 2, 3, 4, 5 (from left to right). These are again high-contrast density plots, where this time the minimal value that appears as black was chosen low enough to highlight …
Figure 10
Figure 10. Figure 10: shows snapshots of the evolution in the case of a perturbation with mφ = 4. These are strikingly similar to the images presented in [10] for the evolution of MP black holes at spins high enough to excite the unstable quadrupole mode (see their figure 6) [PITH_FULL_IM…
Figure 11
Figure 11. Figure 11: Snapshots of time evolution of a ring-like axisymmetric perturbation of the MP black hole with a = 3. The eventual breakdown of axial symmetry is triggered by any generic perturba￾tion, such as numerical noise. Lastly, we consider the possibility of adding the above m…
Figure 12
Figure 12. Figure 12: Snapshots of time evolution of a ‘negative’ ring-like axisymmetric perturbation of the MP black hole (with rotation parameter a = 3). The initial perturbation has amplitude opposite to the one in figure 11, i.e., a bulge at the center, instead of a pinch. 5 Black bar …
Figure 13
Figure 13. Figure 13: Snapshots of time evolution of the fundamental ny = 4 mode added with negative amplitude (i.e., creating a bulge in the middle, instead of a pinch). Since the qualitative evolution of the fundamental symmetric mode has already been described in earlier sections, here …
Figure 14
Figure 14. Figure 14: Deformation of the black bars at their center, as a function of time, for several values of J/M. Perturbations of all unstable bars (J/M > 4/ √ 3) present a phase of exponential growth given by the linear growth rate W of the dominant mode. The zero mode with ny = 4 i…
Figure 15
Figure 15. Figure 15: Growth rate W of the dominant unstable mode of the black bars as a function of J/M. The rates are computed by linear regression of the curves in [PITH_FULL_IMAGE:figures/full_fig_p027_15.png]
Figure 16
Figure 16. Figure 16: Dependence of morigin on the low-mass cutoff , as a function of time, for the two kinds of cutoff introduced in Methods 1 and 2. Method 1 Method 2 0.0001 0.0002 0.0003 0.0004 ϵ 56 58 60 62 64 tbreak [PITH_FULL_IMAGE:figures/full_fig_p035_16.png]
Figure 17
Figure 17. Figure 17: Dependence of tbreak as a function of the low-mass cutoff , for both methods. relatively strong, however, there seems to be a well-defined limit as we approach  = 0. We expect a closely related behaviour for all quantitative results regarding collision final states.…

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Forward citations

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Reviewed August 14, 2026 · model on record in the stance chip above.