PhD Comprehensive Seminar | Brayden Hull, Investigations into Higher Curvature Gravity Theories

MC 5479 

Candidate

Brayden Hull | Applied Mathematics, University of Waterloo

Title

Investigations into Higher Curvature Gravity Theories

Abstract

Theories of higher curvature gravity have been studied by theorists for over half a century. Within these theories, the gravitational action contains terms that are non-linear functions of the   Riemann curvature tensor, deviating from Einstein's General Relativity. These higher curvature theories are of particular interest due to quantum gravity, where it is expected that there will be corrections to the gravitational action that include non-linear curvature terms.  An example of this would be the ability to renormalize a quantum field in a curved spacetime. A particular higher curvature theory of great interest is Lovelock theory, which is discussed as a generalization of Einstein gravity to higher dimensions. It has the unique and elegant property that even though we have non-linear curvature the field equations remain at most differential equations of second order in the metric. 

While black hole solutions have been studied at great lengths in these higher curvature theories, they have been restricted to contain event horizons that possess constant curvature.

This has the advantage that symmetries may be used to simplify the field equations. 

Recently it has been pointed out that this constraint is not necessary, and a solution to the field equations in Lovelock gravity has been discovered that describes a black hole whose event horizon need not be of constant curvature. These black holes have been appropriately called Exotic Black Holes(EBHs).

I have completed several studies of EBHs and discovered several interesting features.

I have shown that horizon geometry greatly influences EBH thermodynamics; in particular, solutions that contain a negative cosmological constant can exhibit a novel triple point at which thermal radiation coexists with two distinct phases (or two distinct sizes) of the black hole at a specific temperature and pressure.

I have also shown that for EBHs in a spacetime with  a positive cosmological can have both zero and negative mass solutions, a phenomenon  not seen before in any theory that contains a positive cosmological constant. This further illustrates how exotic geometries of the horizon can significantly influence the spacetime. Understanding thermodynamics in spacetimes with a positive cosmological constant is a challenge due to the presence of two horizons at unequal temperatures, thereby implying a loss of thermodynamic equilibrium. By placing the black hole in a spherical cavity,

I plan to further investigate EBHs thermodynamics in these scenarios.

 There is also the ambitious task of discovering rotating black hole solutions that have exotic horizons, and I shall carry out an investigation of these solutions as well.

In closing I plan to also investigate a more recently proposed higher curvature theory, called 4-dimensional Einstein Gauss-Bonnet Gravity(4DEGB), which contains quadratic terms in curvature. This theory, discovered a little over 2 years ago, has attracted the attention of physicists due to the fact that in previous attempts to include quadratic curvature into the gravitational action for Einstein gravity (in 4 dimensions) you obtain a total derivative when the action is varied and hence no new dynamics are seen. A detailed study of cosmological large-scale structure has not been properly carried out for this theory, and I will undertake such an investigation.