An introduction to the mechanics of black holes

TL;DR

This paper offers a comprehensive, self-contained introduction to the fundamental laws governing black hole mechanics, including derivations and discussions of related conservation laws in gauge and gravity theories.

Contribution

It provides a detailed, explicit derivation of the laws of black hole mechanics within general relativity, including foundational conservation laws and their implications.

Findings

Derivation of the zeroth, first, and second laws of black hole mechanics

Discussion of conservation laws in gauge and gravity theories

Explicit derivation of the first law in general relativity

Abstract

These notes provide a self-contained introduction to the derivation of the zero, first and second laws of black hole mechanics. The prerequisite conservation laws in gauge and gravity theories are also briefly discussed. An explicit derivation of the first law in general relativity is performed in appendix.