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.