Thermodynamics of spherically symmetric thin-shell spacetimes

Abstract

We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein’s equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of the system: the maximum energy principle applies when we include an entropy term from the singularity of the negative-mass solutions, in addition to the Bekenstein–Hawking term for the entropy of solutions with positive interior mass. Then, the thermodynamic analysis leads to four distinct thermodynamic phases. We also show that all types of solutions can be either thermodynamically stable or dynamically stable, but only solutions with zero interior mass can be both. Since most of our results are analytic, thin shell models emerge as a useful theoretical paradigm for exploring gravitational thermodynamics. Our results provide an additional argument in support of the assignment of entropy to the singularity of negative-mass Schwarzschild spacetimes, and, consequently, to Penrose’s conjecture about the assignment of entropy to singularities.