Abstract
We argue that cosmic censorship is violated in the collision of two black holes in high spacetime dimension D when the initial total angular momentum is sufficiently large. The two black holes merge and form an unstable bar-like horizon, which grows a neck in its middle that pinches down with diverging curvature. When D is large, the emission of gravitational radiation is strongly suppressed and cannot spin down the system to a stable rotating black hole before the neck grows. The phenomenon is demonstrated using simple numerical simulations of the effective theory in the 1/D expansion. We propose that, even though cosmic censorship is violated, the loss of predictability is small independently of D.
Highlights
The cosmic censorship (CC) conjecture [1] raises the question of whether classical gravitational dynamics can drive a low-energy configuration into an accessible regime of quantum gravity, with Planck-scale curvatures and energy densities visible by distant observers
There is convincing evidence of processes that evolve towards CC violation (e.g., [2,3,4]), but the circumstances can vary and important details often remain to be ascertained: are CC violations generic, or do they instead require initial fine-tuning? What is the size of the violation, i.e., the fraction of the initial energy that goes into Planckian densities, and how strong is the loss of classical predictability? Are there any constraints on, or implications for, these violations from thermodynamics and holographic entropy bounds?
Since there is no gravitational radiation, the total angular momentum J is conserved throughout the evolution, which we have checked in our numerics
Summary
The cosmic censorship (CC) conjecture [1] raises the question of whether classical gravitational dynamics can drive a low-energy configuration into an accessible regime of quantum gravity, with Planck-scale curvatures and energy densities visible by distant observers. The addition of spatial dimensions reveals suggestive paths towards the quantum-gravitational regime: Einstein’s theory in dimensions D > 4 contains black strings whose horizons, resembling fluid jets that break up into droplets, are unstable to growing inhomogeneities along their length, with necks pinching where spacetime curvature diverges [3, 5]. Beyond a certain value of the spin, this configuration is unstable in a manner similar to the instability that drives black strings towards a CC-violating break up [6], i.e., the bar forms a neck in its middle that pinches down with diverging curvature.
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