Phenomenological Description of the Interior of the Schwarzschild Black Hole

Understand

We discuss a sufficiently large 4-dimensional Schwarzschild black hole which is in equilibrium with a heat bath.

• In other words, we consider a black hole which has grown up from a small one in the heat bath adiabatically.
• We express the metric of the interior of the black hole in terms of two functions: One is the intensity of the Hawking radiation, and the other is the ratio between the radiation energy and the pressure in the radial direction.
• Especially in the case of conformal matters we check that it is a self-consistent solution of the semi-classical Einstein equation, $G_{\mu\nu}=8\pi G \langle T_{\mu\nu}\rangle$.