Black Hole Entropy from Non-dirichlet Sectors, and a Bounce Solution

Abstract

In a series of recent works the relevance of gravitational boundary degrees of freedom and their dynamics in gravity quantization and black hole information has been explored. In this work we further the progress by keenly focusing on the boundary degrees of freedom as the origin of black hole entropy. Wald's entropy formula is scrutinized, and the reason that the Wald's formula correctly captures the entropy of a black hole is examined. Afterwards, limitations of the Wald's method are discussed; a coherent view of entropy based on boundary dynamics is presented. The discrepancy observed in the literature between holographic and Wald's entropies is addressed. We generalize the entropy definition so as to handle a time-dependent black hole. Large gauge symmetry plays a pivotal role. Non-Dirichlet boundary conditions and gravitational analogues of Coleman-De Luccia bounce solutions are central in identifying the microstates and differentiating the origins of entropies associated with different classes of solutions. The result in the present work leads to a view that black hole entropy is entanglement entropy in a thermodynamic setup.

On the covariant formulation of gauge theories with boundaries

“…The UCA charges have support on a boundary located at a finite distance, as is the case for the quantum Hall effect discussed above. They are believed to play an important role in gauge theories, holography, black hole physics, quantum gravity and much more [85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104]. One of the most intriguing areas in which they are believed to play a role is entanglement entropy.…”