The Atmosphere of a Black Hole

TL;DR

This paper develops a static, isotropic fluid model around a black hole, analyzing its effects on spacetime structure, and derives related physical properties, revealing behavior akin to radiation near the core and dust at large distances.

Contribution

It introduces a new static, isotropic fluid solution around a black hole and explores its physical implications and limitations.

Findings

Near the black hole, the solution behaves as radiation with p=ρ/3.

Far from the black hole, the solution behaves as dust with p=0.

Derived density, pressure, temperature, and equation of state parameters.

Abstract

We present a static, isotropic fluid solution around a black hole and its effects on the field equations and the horizon. We offer the solutions, their descriptions and we comment on their shortcomings. We derive from the proposed metric the density, the pressure, the equation of state, the temperature near and far of the black hole and the equation of state parameter. We show that for a special case, when $r\rightarrow\ 0$ the solution behaves as $p=\frac{\rho}{3}$, the equation of state for radiation and for $r\rightarrow\infty$ we observe that $p=0$, the equation of state for dust.