Evidence for violations of Weak Cosmic Censorship in black hole collisions in higher dimensions

Abstract

We study collisions of boosted rotating black holes in D = 6 and 7 spacetime dimensions with a non-zero impact parameter. We find that there exists an open set of initial conditions such that the intermediate state of the collision is a black hole with a dumbbell-like horizon which is unstable to a local Gregory-Laflamme-type instability. We are able to provide convincing numerical evidence that the evolution of such an instability leads to a pinch off of the horizon in finite asymptotic time thus forming a naked singularity, as in similar unstable black holes. Since the black holes in the initial state are stable, this is the first genuinely generic evidence for the violation of the Weak Cosmic Censorship Conjecture in higher dimensional asymptotically flat spacetimes.

Lessons for adaptive mesh refinement in numerical relativity

“…By comparing the BH simulations with those from the box-in-a-box based Lean code, we demonstrate that with an appropriate choice of tagging criteria, AMR simulations reach the same accuracy and convergence as state-of-the-art BH binary codes using Cartesian grids. While AMR does not directly bestow major benefits on the modeling of vacuum BH binaries (and is typically more computationally expensive), it offers greater flexibility in generalizing these to BH spacetimes with scalar or vector fields, other forms of matter, or BHs of nearly fractal shape that can form in higher-dimensional collisions [36]. The simulations of rapidly oscillating or gravitationally collapsing scalar fields demonstrate GRChombo's capacity to evolve highly compact and dynamic matter configurations of this type.…”

“…One key advantage is that one does not need to know a priori the mass of the BH spacetime which forms, and it can be seen that simply using the j = 0 values will give a conservative coverage of the horizon. These types of criteria were used extensively in the higher dimensional black ring spacetimes studies in [36][37][38][39] and for the investigation into gravitational collapse in a modified gravity theory in [35].…”

“…In contrast to the moving boxes approach, this approach allows for highly flexible 'manyboxes-in-many-boxes' mesh topologies, enabling the study of dynamical systems where the spacetime dynamics are not driven by localized compact systems e.g. in studying non spherical collapse scenarios [32,33], higher dimensional BHs/black string evolution [34][35][36][37][38][39], cosmic string evolution [40][41][42], and the behaviour of strongly inhomogeneous cosmological spacetimes [43][44][45][46][47][48][49][50][51].…”

The Large D Limit of Einstein's Equations

“…(Andrade et al, 2019a) perform a detailed estimate where they argue that, very likely down to at least D 8, radiation will be a negligible effect, and the dynamical instability will break up the bar into two disks. Their estimates are not precise enough to conclude if the effect will persist for lower D, but dedicated numerical simulations indicate that it does, even in D = 6 (Andrade et al, 2020). The arguments in (Andrade et al, 2019a,b) are based on the similarity between the instabilities of black bars and of black strings, and the latter exist down to D = 5.…”

Numerical relativity for Horndeski gravity

“…where x is a distance measure from the "center" of the black hole to the apparent horizon, and x, w are pre-set constants k . As a measure of the distance inside the black hole, Figueras and França used the value of the conformal factor χ in the CCZ4 formulation, the level sets of which have been empirically shown to closely follow the apparent horizons of black hole and black strings 184,185 (for example, for Schwarzschild black holes in moving puncture gauge, within the CCZ4 formulation the black hole apparent horizon settles to around χ ∼ 0.25 39 ).…”