Date of Award
Program or Major
Doctor of Philosophy
The study of black hole thermodynamics has provided deep insights into the nature of quantum gravity. In particular, it is almost universally accepted nowadays that 'quantum gravity is holographic', so that the maximum amount of information allowed in a given region of spacetime is proportional to the area of the boundary rather than the volume of the region. This is against the conventional notion of extensivity of information (entropy), but in accord with Bekenstein's proposal on the proportionality of black hole entropy to its event horizon area. Due to the very definition of black holes, however, conventional black hole thermodynamics rely on the standard causal structure of general relativity dictated by local light cones. It may therefore seem that the notion of holography is ultimately tied to the same causal structure, and hence, on the equivalence principle and local Lorentz invariance.
The goal of this dissertation is to re-evaluate this generally accepted wisdom. To that end, we consider a modified gravity theory called Einstein-aether theory. This theory violates local Lorentz invariance and therefore destroys the notion of a universal light cone. Yet, in the low energy limit, it possesses static and spherically symmetric solutions with 'universal horizons'---spacelike hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, this theory admits black hole solutions but with very different causal structures.
In this dissertation, we investigate into how much of black hole thermodynamics carry over in this new setting. We consider static and spherically symmetric black hole solutions of Einstein-aether theory and establish the Smarr formula and the first law of black hole mechanics for them, with the relevant horizon now the universal horizon. We also consider tunneling of a scalar 'test' field through the universal horizon, and show that the latter radiates as a blackbody at a fixed temperature. Our results suggest that the scope of holography may be much broader than currently assumed. However, one still needs to go a long way before these questions are convincingly settled, and we comment on the open questions in our concluding remarks.
Bhattacharyya, Jishnu, "Aspects of holography in Lorentz-violating gravity" (2013). Doctoral Dissertations. 729.