Geometric Entropy

TL;DR

This paper explores the geometric nature of black hole entropy, focusing on Wald's formulation within covariant gravity theories, and distinguishes between kinematic and dynamical thermodynamic laws.

Contribution

It clarifies the inputs and dependencies of Wald's entropy formalism and differentiates between kinematic and dynamical thermodynamic laws in black hole physics.

Findings

Wald's entropy depends on the specific form of the gravitational action.

The derivation of thermodynamic laws reveals where the action's form influences the laws.

The work emphasizes the geometric interpretation of black hole entropy.

Abstract

The laws of mechanics of stationary black holes bear a close resemblance with the laws of thermodynamics. This is not only a mathematical analogy but also a physical one that helps us answer deep questions related to the thermodynamic properties of the black holes. It turns out that we can define an entropy which is purely geometrical for black holes. In this thesis we explain Wald's formulation which identifies black hole entropy for an arbitrary covariant theory of gravity. We would like to know precisely what inputs go into arriving at Wald's formalism. This expression for the entropy clearly depends on the precise form of the action. The secondary theme of this thesis is to distinguish thermodynamic laws which are kinematic from those which are dynamical. We would like to see explicitly in the derivation of these laws, where exactly the form of action plays a role. In the beginning we motivate the definition of entropy using the Einstein-Hilbert Lagrangian. We encounter the Zeroth law, the Hawking radiation, the second law, and then Wald's formulation.