Near-Horizon Black Hole Physics

Citation

Chen, Baoyi (2022) Near-Horizon Black Hole Physics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8szr-9e68. https://resolver.caltech.edu/CaltechTHESIS:08172021-040557487

Abstract

This thesis studies the near-horizon black hole physics in depth from three perspectives.

An important tool for studying perturbations of black hole spacetime is the linearized Einstein equations (LEE). In the Kerr spacetime, the variables in LEE do not separate, which poses a lot of difficulties to obtaining analytical solutions. By taking the near-horizon limit of extremal Kerr black holes, additional symmetries emerge to make the LEE separable. This is achieved by decomposing the metric perturbations using some basis functions adapted to the symmetry. I further show that in two string-inspired low-energy effective theories of gravity, LEE can be directly solved and analytical black hole solutions can be found.

Naively, the near-horizon perturbations of an extremal black hole may destroy the horizon and make the singularity expose itself. This is a direct challenge of the weak cosmic censorship conjecture (WCCC). Based on Wald’s gendanken experiments to destroy black holes, I examine the WCCC for the extremal charged black hole in possible generalizations of Einstein-Maxwell theory due to the higher-order corrections, up to fourth-derivative terms. It turns out that, provided the null energy condition for the falling matter, the WCCC is preserved for all possible generalizations. I further find that for BTZ black holes, i.e. solutions to (2+1)-Einstein gravity with asymptotically AdS₃ boundary, WCCC is always preserved. Through the AdS/CFT correspondence, this establishes the connections between black hole thermodynamics and WCCC.

From considerations of quantum gravity and quantum information, it has been conjectured that space-time geometry near the horizon can be modified, even at scales larger than the Planck scale. The resulting spacetime is commonly referred to as the exotic compact object (ECO). A viable method to look for the near- horizon quantum structures is searching for gravitational wave echoes in the GW signals. After discussing the stability issues associated with the ECOs, I build up the phenomenology for gravitational echoes. I also introduce a new framework to deal with the near-horizon boundaries by considering the tidal response of the ECO as experienced by zero-angular-momentum fiducial observers. It is then straightforward to apply the boundary condition to computing gravitational-wave echoes from exotic compact objects.

Thesis Files