Semiclassical corrections to a regularized Schwarzschild metric

Abstract

A version of the Schwarzschild metric to be valid in microphysics is proposed. The source fluid is anisotropic with $p_{r} = -\rho$ and fluctuating tangential pressures. At large distances with respect to the Compton wavelength associated to the source particle, they do not depend on the mass $m$ of the source and everywhere depend on $\hbar$ and the velocity of light $c$ but not on the Newton constant $G$. The particle may be a black hole for $m \geq m_{P}$ only and when $m = m_{P}$ it becomes an extremal black hole. The Komar energy $W$ of the gravitational fluid is $mc^{2}$ for $\hbar = 0$ and at large distances and vanishes at $r_{0} = 2\hbar/emc$. The WEC is violated when $r < r_{0}/2$ due to the negative tangential pressures. The horizon entropy for the extremal black hole is finite though $W$ and the temperature $T$ are vanishing there.