Thermo field dynamics approach for entropy of spacetime

TL;DR

This paper proposes a thermo field dynamics method to compute the entropy of various spacetimes by relating it to the entropy of a thermo quantum field at the same temperature, using the thermo vacuum state.

Contribution

It introduces a novel thermo field dynamics approach to calculate spacetime entropy, linking it to thermo quantum fields and the maximal manifold vacuum state.

Findings

Entropy of spacetime equals the entropy of a thermo quantum field at the same temperature.

The approach is exemplified on Rindler, Milne, Boulware, and Minkowski spacetimes.

Entropy is computed as an expectation value of the entropy operator on a thermo vacuum state.

Abstract

A thermo field dynamics approach for calculating the entropy of a spacetime is suggested. It is exemplified through the Rindler spacetime, the Milne spacetime, the Boulware spacetime, and the Minkowski spacetime with a moving mirror that the entropy of a spacetime is equal to the entropy of a thermo quantum field with the same temperature of the spacetime we study. This in fact suggests an thermo field dynamics approach of calculating the entropy of a spacetime. In this approach, the entropy of a spacetime is an expectation value of the entropy operator on a thermo vacuum state. The thermo vacuum state is the vacuum state on the maximal manifold which is the maximal analytic extension of the spacetime we study.