Nontriviality in Black Hole Thermodynamics: towards physically and mathematically rigorous foundation as phenomenology

TL;DR

This paper investigates the foundational differences between black hole thermodynamics and laboratory thermodynamics, highlighting the nontrivial assumptions involved and proposing a rigorous axiomatic framework for black hole thermodynamics.

Contribution

It identifies key assumptions that do not hold for black holes and proposes a set of basic assumptions to establish a rigorous phenomenological foundation.

Findings

Certain laboratory thermodynamics assumptions fail for black holes

Proposed axioms aim to rigorously underpin black hole thermodynamics

Clarifies the nontrivial aspects of black hole thermodynamic principles

Abstract

Comparing black hole thermodynamics with the axiomatic formulation of thermodynamics for laboratory systems, it is found that some basic assumptions (required by experimental facts) in laboratory thermodynamics do not hold for black hole thermodynamics. Hence, at present, it is not obvious whether black hole thermodynamics retains some crucial theorems of laboratory thermodynamics (e.g. Carnot's theorem, increase of entropy by arbitrary adiabatic process, and uniqueness of entropy) whose proofs use the basic assumptions which do not hold for black holes. This paper aims to clarify such nontriviality in black hole thermodynamics, and propose a suitable set of basic assumptions in black hole thermodynamics, which are regarded as the rigorous foundation of black hole thermodynamics as phenomenology.