Thermodynamics of quantum photon spheres

TL;DR

This paper develops a semiclassical thermodynamic model for quantum photon spheres, deriving their energy spectra and spectral energy density, revealing unusual thermodynamic properties that could produce unique observational signatures.

Contribution

It introduces a novel semiclassical framework for quantum photon spheres, deriving their energy spectra and thermodynamic behavior, which has not been previously explored.

Findings

Photon spheres exhibit nonusual thermodynamic properties when thermalized.

Derived spectral energy density of radiation emitted by photon spheres.

Potential for distinct observational signatures from photon spheres.

Abstract

Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.