We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected by necks which become ever thinner over time.

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured BergerRigoutsos grid generation. The code supports non-trivial "many-boxes-in-many-boxes" mesh hierarchies and massive parallelism through the Message Passing Interface (MPI). GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, whilst also significantly simplifying the process of setting up the mesh for these problems. We show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.

We propose a model-free deep reinforcement learning method that leverages a small amount of demonstration data to assist a reinforcement learning agent. We apply this approach to robotic manipulation tasks and train end-to-end visuomotor policies that map directly from RGB camera inputs to joint velocities. We demonstrate that our approach can solve a wide variety of visuomotor tasks, for which engineering a scripted controller would be laborious. In experiments, our reinforcement and imitation agent achieves significantly better performances than agents trained with reinforcement learning or imitation learning alone. We also illustrate that these policies, trained with large visual and dynamics variations, can achieve preliminary successes in zero-shot sim2real transfer. A brief visual description of this work can be viewed in this video.

We determine the end point of the axisymmetric ultraspinning instability of asymptotically flat Myers-Perry black holes in D = 6 spacetime dimensions. In the non-linear regime, this instability gives rise to a sequence of concentric rings connected by segments of black membrane on the rotation plane. The latter become thinner over time, resulting in the formation of a naked singularity in finite asymptotic time and hence a violation of the weak cosmic censorship conjecture in asymptotically flat higher-dimensional spaces.Introduction.-The recent detection of gravitational waves from black hole binary mergers [1,2] has provided the first direct observation of these objects. The current observational data are compatible with the predictions of general relativity, and they suggest that the end point of such mergers is a Kerr black hole (BH) [3]. These observations provide evidence that the Kerr BH in vacuum is non-linearly stable, at least within a certain range of the angular momentum. However, a mathematically rigorous understanding of the stability of the generic Kerr BH, as well as a thorough understanding of its dynamics under arbitrary perturbations, is still lacking. In fact, recent work suggests that novel and nontrivial dynamics may be present very close to extremality (e.g., [4][5][6]).Higher dimensional BHs, however, can be unstable under gravitational perturbations. This was first shown by Gregory and Laflamme (GL) for black strings and black p-branes [7]. Determining the end point of this instability has been a subject of intense study due to the potential implications on the weak cosmic censorship conjecture (WCC) in such spacetimes. With the aid of numerical relativity (NR), [8] found that the GL instability gives rise to a self-similar structure of bulges connected by ever thinner string segments, which all undergo the GL instability. Eventually, the black string pinches off in finite asymptotic time, resulting in a naked singularity. Since no fine-tuning of the initial data was required, this result constituted a violation of the WCC, albeit in spacetimes with compact extra dimensions.Contrary to the D = 4 case, asymptotically flat BHs in higher dimensions can carry arbitrarily large angular momenta. At very large angular momenta, BHs become highly deformed and resemble black branes, which are known to be unstable under the GL instability [9]. This observation highlighted the possibility that higher dimensional asymptotically flat BHs can be unstable under gravitational perturbations. This indeed turned out to be the case. For instance, the black rings of [10] suffer from various types of instabilities [11][12][13][14][15][16], including the GL instability. The non-linear evolution of the latter was studied in a very recent work by three of us [15], where it was found that, for sufficiently thin rings, the evolution of the instability is similar to that of the GL instability of black strings. Hence, a naked singularity should form in finite asymptotic time, thus violating the WCC in higher-dimensio...

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