Research Projects

The proposal aims to construct a proof of the second law of black hole thermodynamics in diffeomorphism invariant theories of gravity beyond general relativity. These theories serve as the effective low-energy limit of any consistent UV complete quantum theory of gravity. The dynamical black hole geometries should continue to be a solution to the equations of motion, with small fluctuations around a stationary black hole modeling the dynamical situation. Using geometric knowledge about the space-time metric of the fluctuating black hole, an entropy current with non-negative divergence is constructed. This schematic supports an intuitive schematic for how the dynamical black hole should equilibrate, supporting an intuitive schematic for entropy production and spatial movement or flow on constant time slices of the horizon. The researchers aim to extend this construction to higher orders in the amplitude expansion, such as non-perturbative processes like black hole mergers. They also want to understand if this can be matched with the entropy current obtained using the fluid gravity correspondence, which may have implications for the membrane paradigm. Lastly, they aim to apply this formalism to studying holographic entanglement entropy using gauge gravity duality techniques. This duality states that a theory of quantum gravity in bulk with a non-gravitating field theory residing on the boundary of this bulk theory can be equivalence. The geometric structure of space-time around a minimal area surface should provide essential insights regarding holographic entanglement entropy. This knowledge could give an independent understanding of how the bulk equations of motion can be derived from entanglement entropy dynamics in the boundary theory.