Entropy of a Wormhole from the Constituent

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.