Black Hole Radiation and Volume Statistical Entropy

Abstract

The simplest possible equation for Hawking radiation $P_{{\rm SH}} =\frac{{G\rho\, \hbar }}{{90}}$ and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S _bh∝ (kAc ³)/ℏ G. Variations of S _bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R _H, p = ${\frac{3}{{2\pi }}})\frac{\hbar}{{R_{\rm H} }}$which is similar tothe Compton wavelength relation.