Self-Screening Hawking Atmosphere in the Presence of a Bulk Viscosity

TL;DR

This paper extends 't Hooft's black hole model by incorporating bulk viscosity into the matter envelope, demonstrating that even small viscosity can align the model with Hawking entropy if the equation of state parameter is near 4/3.

Contribution

It generalizes 't Hooft's theory to include bulk viscosity, showing how it affects the black hole entropy calculation and the equation of state parameter.

Findings

Positive bulk viscosity aligns the model with Hawking entropy.

The equation of state parameter must be slightly less than 4/3.

Even small viscosity significantly impacts the model's agreement with Hawking's formula.

Abstract

The recent theory of 't Hooft [ Nucl. Phys. Suppl. {\bf 68}, 174 (1998)] models the black hole as a system endowed with an envelope of matter that obeys an equation of state in the form $ p=(\gamma -1)\rho$, and acts as a source in Einstein's equations. The present paper generalizes the 't Hooft theory so as to take into account a bulk viscosity $\zeta$ in the fluid. It is shown that even a slight positive value of $\zeta$ will suffice to yield complete agreement with the Hawking formula for the entropy of the black hole, if the value of the constant $\gamma$ takes a value that is slightly less than 4/3. The value $\gamma=4/3$ corresponds to a radiation fluid.