The Thermodynamics of Black Holes

TL;DR

The paper surveys the landscape of black hole thermodynamics, showing how classical black hole mechanics parallels thermodynamics and how quantum effects yield a physical temperature via Hawking radiation with $T = κ/(2π)$. It argues for the generalized second law with $S' = S_{ ext{outside}} + S_{ m bh}$ and discusses entropy bounds, including the holographic limit $S \\le A/4$, and multiple approaches to deriving black hole entropy, such as Euclidean gravity, entanglement entropy, loop quantum gravity, string theory, and conformal field theory methods. While substantial progress links gravitational dynamics, quantum fields, and thermodynamics, open issues remain, notably the black hole information paradox and the precise microscopic degrees of freedom behind $S_{ m bh}$, with potential insights across multiple frameworks. The work emphasizes that a deeper quantum gravity framework is needed to fully understand entropy, information preservation, and the fundamental nature of horizon degrees of freedom. The results collectively reinforce the view that black holes are thermodynamic objects whose entropy scales with horizon area, offering a testing ground for quantum gravity proposals and holographic ideas.

Abstract

We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black hole entropy. We conclude with a discussion of some unresolved open issues.