A generic relation between baryonic and radiative energy densities of stars

TL;DR

This paper derives a universal relation between radiation and baryonic energy densities in stars, showing how this ratio depends on gravitational parameters and redshift, with implications for gravitational collapse and black hole formation.

Contribution

It introduces a simple, general relation between radiation and baryonic energy densities applicable in Newtonian and relativistic regimes, linking these to gravitational redshift during collapse.

Findings

In the Newtonian limit, rho_r/rho_0 ~ GM/Rc^2.

In the relativistic limit, rho_r/rho_0 ~ (1+z).

During collapse, matter may become an extremely hot fireball despite low observed luminosity.

Abstract

By using elementary astrophysical concepts, we show that for any self-luminous astrophysical object, the ratio of radiation energy density inside the body (rho_r) and the baryonic energy density (rho_0) may be crudely approximated, in the Newtonian limit, as rho_r/rho_0 ~ GM/Rc^2, where G is constant of gravitation, c is the speed of light, M is gravitational mass, and R is the radius of the body. The key idea is that radiation quanta must move out in a diffusive manner rather than free stream inside the body of the star. When one would move to the extreme General Realtivistic case i.e., if the surface gravitational redshift, z >> 1, it is found that, rho_r/rho_0 ~ (1+z). Previous works on gravitational collapse, however, generally assumed rho_r/rho_0 << 1. On the other hand, actually, during continued general relativistic gravitational collapse to the Black Hole state (z --> infty), the collapsing matter may essentially become an extremely hot fireball a la the very early universe even though the observed luminosity of the body as seen by a faraway observer, L^\infty ~ (1+z)^{-1} --> 0 as z --> infty, and the collapse might appear as ``adiabatic''.