Charge Conservation, Entropy Current, and Gravitation

TL;DR

This paper introduces a new vector field-based method to define conserved charges and entropy currents in general field theories and gravitational systems, linking conservation laws with thermodynamics.

Contribution

It demonstrates the existence of a conserved charge and entropy current without requiring global symmetry, applicable to various gravitational backgrounds.

Findings

Conserved charge satisfies the first law of thermodynamics.

Entropy density remains conserved during isotropic universe expansion.

Black hole entropy matches Bekenstein-Hawking entropy with thermodynamic consistency.

Abstract

We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.