Mass and temperature limits for blackbody radiation

TL;DR

This paper investigates the mass and temperature limits of blackbody radiation spheres under gravitational effects, revealing specific bounds for mass and density when the radius is fixed, and explores entropy profiles related to these parameters.

Contribution

It provides the first analysis of mass and temperature limits for blackbody radiation spheres considering gravitational self-interaction effects.

Findings

No absolute mass or temperature limit exists without fixed radius.

Limits on mass and density depend on the sphere's radius, with specific bounds derived.

Entropy profiles vary with mass and temperature, influencing thermodynamic properties.

Abstract

A spherically symmetric distribution of classical blackbody radiation is considered, at conditions in which gravitational self-interaction effects become not negligible. Static solutions to Einstein field equations are searched for, for each choice of the assumed central energy density. Spherical cavities at thermodynamic equilibrium, i.e. filled with blackbody radiation, are then studied, in particular for what concerns the relation among the mass M of the ball of radiation contained in them and their temperature at center and at the boundary. For these cavities it is shown, in particular, that: i) there is no absolute limit to M as well to their central and boundary temperatures; ii) when radius R is fixed, however, limits exist both for mass and for boundary energy density rho_B: M <= K M_S(R) and rho_B <= Q/R^2, with K = 0.493 and Q = 0.02718, dimensionless, and M_S(R) the Schwarzschild mass for that radius. Some implications of the existence and the magnitude of these limits are considered. Finally the radial profiles for entropy for these systems are studied, in their dependence on the mass (or central temperature) of the ball of radiation.