In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial many-boxes-in-many-boxes mesh hierarchi
es 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 construct five dimensional black rings in global anti-de Sitter space using numerical methods. These rings satisfy the BPS bound $| J | < M ell$, but the angular velocity always violates the Hawking-Reall bound $| Omega_H ell | leq 1$, indicating
that they should be unstable under superradiance. At high temperatures, the limit $| Omega_H ell | searrow 1$ is attained by thin rings with an arbitrarily large radius. However, at sufficiently low temperatures, this limit is saturated by a new kind of rings, whose outer circle can still be arbitrarily long while the hole in the middle does not grow proportionally. This gives rise to a membrane-like horizon geometry, which does not have an asymptotically flat counterpart. We find no evidence for thin AdS black rings whose transverse $S^2$ is much larger than the radius of AdS, $ell$, and thus these solutions never fall into the hydrodynamic regime of the dual CFT. Thermodynamically, we find that AdS black rings never dominate the grand canonical ensemble. The behaviour of our solutions in the microcanonical ensemble approaches known perturbative results in the thin-ring limit.
In this paper we numerically construct localised black hole solutions at the IR bottom of the confining geometry of the AdS soliton. These black holes should be thought as the finite size analogues of the domain wall solutions that have appeared prev
iously in the literature. From the dual CFT point of view, these black holes correspond to finite size balls of deconfined plasma surrounded by the confining vacuum. The plasma ball solutions are parametrised by the temperature. For temperatures well above the deconfinement transition, the dual black holes are small and round and they are well-described by the asymptotically flat Schwarzschild solution. On the other hand, as the temperature approaches the deconfinement temperature, the black holes look like pancakes which are extended along the IR bottom of the space-time. On top of these backgrounds, we compute various probes of confinement/deconfinement such as temporal Wilson loops and entanglement entropy.
We use AdS/CFT to construct the gravitational dual of a 5D CFT in the background of a non-extremal rotating black hole. Our boundary conditions are such that the vacuum state of the dual CFT corresponds to the Unruh state. We extract the expectation
value of the stress tensor of the dual CFT using holographic renormalisation and show that it is stationary and regular on both the future and the past event horizons. The energy density of the CFT is found to be negative everywhere in our domain and we argue that this can be understood as a vacuum polarisation effect. We construct the solutions by numerically solving the elliptic Einstein--DeTurck equation for stationary Lorentzian spacetimes with Killing horizons.
