Entropy of a Wormhole from the Constituent

TL;DR

This paper derives the entropy of static spherically symmetric wormholes based on their matter content, analyzing specific solutions and highlighting the role of ADM mass combinations in wormhole thermodynamics.

Contribution

It introduces a method to compute wormhole entropy from matter entropy and explores the significance of ADM mass combinations in their thermodynamics.

Findings

Exact wormhole entropies are obtained for specific solutions.

Asymptotic entropy forms are characterized for regular solutions.

The ADM mass combination influences wormhole thermodynamic properties.

Abstract

We obtain the entropy of a static spherically symmetric wormhole from the entropy of matter consisting it. Some exact wormhole solutions are analyzed in detail and their entropies are obtained. We display the asymptotic forms of the entropy for solutions having regular asymptotic regions in which matter spreads to infinity. In the analysis, we find that the combination of ADM masses $\mathcal{M}\equiv \alpha_+ M_+ + \alpha_- M_-$ plays an important role in thermodynamics of a wormhole, where $\displaystyle \alpha_\pm \equiv \lim_{r\to \infty} \sqrt{-g_{tt}}$ in the upper/lower half, respectively.