CFTs in rotating black hole backgrounds

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.Comment: 20 + 13 pages, 3 appendices. (Updated to match the content of published version. One extra appendix added.

Applications of Numerical Relativity Beyond Astrophysics

Numerical relativity has proven to be a successful and robust tool for non-perturbative studies of gravitational phenomena in the highly dynamical and/or non-linear regime. Perhaps the most prominent achievement in the field is the breakthrough success in simulating the merger of binary black hole systems. Gravitational waveforms resulting from these simulations serve as precise theoretical predictions of general relativity, which can be tested against observational data, such as those recently made by the LIGO experiment. This dissertation explores applications of numerical relativity which lie beyond the realm of astrophysics. One motivation for this comes from the AdS/CFT correspondence, which allows us to study strongly coupled quantum field theories by considering classical gravity with a negative cosmological constant. More concretely, we construct stationary asymptotically anti-de Sitter spacetimes by numerically solving the Einstein equations in a strongly elliptic form, subject to various boundary conditions corresponding to the physical setting of interest. Three applications of this technique are presented here. 1) A toroidal “black ring” in global AdS5, which provides a more complete phase diagram for AdS5 black holes. 2) A black hole on an AdS soliton background, which is dual to a localised ball of deconfined plasma surrounded by confined matter. 3) A rotating horizon extending to the AdS boundary, which allows us to the study the behaviour of the CFT in the presence of a rotating black hole. Outside of AdS/CFT, time-dependent numerical relativity in higher dimensions can also inform inquiries into the mathematical properties of general relativity as a theory of gravity. In particular, long, thin black hole horizons are known to be subject to the Gregory–Laflamme instability, and this is expected to result in an eventual violation of the weak cosmic censorship conjecture. A landmark simulation of the black string confirmed this in the Kaluza–Klein setting, however the generalisation of this setup to asymptotically flat black rings poses new challenges for numerical relativity. Even after a successful simulation, the resulting apparent horizons possess nontrivial geometries which are problematic for existing horizon finding methods. This dissertation also covers aspects of technical development in the GRChombo adaptive mesh refinement code which were necessary for the successful evolution and analysis of a black ring instability

End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture.

This is the author accepted manuscript. The final version is available at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.071102#fulltext.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.We are very grateful to Garth Wells (Dept. Engineering, U. Cambridge) for suggesting to us the shock capturing technique which has proven so valuable in this work. We would like to thank J. Briggs, J. Camps, R. Emparan, J. Jäykkä, K. Kornet, L. Lehner, F. Pretorius, H. Reall, E. Schnetter, U. Sperhake, T. Wiseman and H. Witek for numerous stimulating discussions. P.F. would like to especially thank E. Schnetter and U. Sperhake for early collaboration in this project. We are very grateful to our collaborators and co-developers of the GRC HOMBO code, K. Clough, E. Lim and H. Finkel. We would also like to thank J. Santos and B. Way for allowing us to display their data in Fig. 1. A significant part of this work was undertaken on the COSMOS Shared Memory system at DAMTP, University of Cambridge, operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital Grant No. ST/J005673/1 and STFC Grants No. ST/H008586/1, No. ST/K00333X/1. Further portions of this research were conducted with high performance computational resources provided by Louisiana State University [31] on its SuperMike-II cluster under allocation NUMREL06. The authors also acknowledge HPC resources from the NSF-XSEDE Grant No. PHY-090003, provided by the Texas Advanced Computing Center (TACC) at The University of Texas at Austin on its Stampede cluster, and by the San Diego Supercomputer Center (SDSC) at UC San Diego on its Comet cluster. P.F. and S.T. were supported by the European Research Council Grant No. ERC-2011-StG 279363- HiDGR. P.F. was also supported by the Stephen Hawking Advanced Research Fellowship from the Centre for Theoretical Cosmology, University of Cambridge. P.F. is currently supported by a Royal Society University Research Fellowship and by the European Research Council Grant No. ERC-2014-StG 639022-NewNGR. MK is supported by an STFC studentship. P.F. wants to thank Perimeter Institute and Princeton University for hospitality during various stages of this work

GRChombo : Numerical Relativity with Adaptive Mesh Refinement

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 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.Comment: 48 pages, 24 figure

Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization

We present in detail the Einstein equations in the Baumgarte–Shapiro–Shibata–Nakamura formulation for the case of D-dimensional spacetimes with SO(D−d)isometry based on a method originally introduced in Ref. 1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value d = D − 2, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in D = 7 spacetime dimensions with SO(4) symmetry.U.S. is supported by the H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” grant agreement No. MaGRaTh–646597, the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904, the STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet and TACC Stampede clusters through NSF-XSEDE Award Nos. PHY-090003, the Cambridge High Performance Computing Service Supercomputer Darwin using Strategic Research Infrastructure Funding from the HEFCE and the STFC, and DiRAC’s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1. P.F. and S.T. are supported by the H2020 ERC Starting Grant “New frontiers in numerical general relativity” grant agreement No. NewNGR- 639022. P.F. is also supported by a Royal Society University Research Fellowship. W.G.C. and M.K. are supported by STFC studentships.This is the final version of the article. It first appeared from the World Scientific Publishing Company via http://dx.doi.org/10.1142/S021827181641013

Predictive Sampling: Real-time Behaviour Synthesis with MuJoCo

We introduce MuJoCo MPC (MJPC), an open-source, interactive application and software framework for real-time predictive control, based on MuJoCo physics. MJPC allows the user to easily author and solve complex robotics tasks, and currently supports three shooting-based planners: derivative-based iLQG and Gradient Descent, and a simple derivative-free method we call Predictive Sampling. Predictive Sampling was designed as an elementary baseline, mostly for its pedagogical value, but turned out to be surprisingly competitive with the more established algorithms. This work does not present algorithmic advances, and instead, prioritises performant algorithms, simple code, and accessibility of model-based methods via intuitive and interactive software. MJPC is available at: github.com/deepmind/mujoco_mpc, a video summary can be viewed at: dpmd.ai/mjpc.Comment: Minor fixes and formattin