The Atmosphere of a Black Hole

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.