Hot Spaghetti: Viscous Gravitational Collapse

TL;DR

This paper investigates the internal dynamics of matter collapsing into a black hole using viscous relativistic hydrodynamics, revealing conditions under which viscous models break down during gravitational collapse.

Contribution

It introduces a viscous hydrodynamic framework to analyze matter collapse into black holes and identifies failure conditions of this approach.

Findings

Viscous hydrodynamics fails when dissipative radial pressure exceeds thermal pressure.

Failure occurs when radial pressure becomes negative.

Breakdown happens when tidal force variation timescale is shorter than hydrodynamic response time.

Abstract

We explore the fate of matter falling into a macroscopic Schwarzschild black hole for the simplified case of a radially collapsing thin spherical shell for which the back reaction of the geometry can be neglected. We treat the internal dynamics of the infalling matter in the framework of viscous relativistic hydrodynamics and calculate how the internal temperature of the collapsing matter evolves as it falls toward the Schwarzschild singularity. We find that viscous hydrodynamics fails when either, the dissipative radial pressure exceeds the thermal pressure and the total radial pressure becomes negative, or the time scale of variation of the tidal forces acting on the collapsing matter becomes shorter than the characteristic hydrodynamic response time.