Anisotropic fluid with time dependent viscosity coefficients

TL;DR

This paper models the interior of a Schwarzschild black hole using an anisotropic, viscous fluid with time-dependent coefficients, satisfying energy conditions and exhibiting dark energy-like properties.

Contribution

It introduces a novel anisotropic fluid model with time-dependent viscosity for black hole interiors, satisfying all energy conditions and featuring unique pressure and viscosity characteristics.

Findings

The interior geometry has an instantaneous Minkowski form.

The fluid obeys an equation of state similar to dark energy.

Viscosity coefficients are time-dependent and anisotropic.

Abstract

A spacetime endowed with an anisotropic fluid is proposed for the interior of a Schwarzschild black hole. The geometry has an instantaneous Minkowski form and is a solution of Einstein's equations with a stress tensor on the r.h.s. obeying all the energy conditions. The interior fluid is compressible, with time dependent shear and bulk viscosity coefficients. The energy density $\rho$ and the ''radial'' pressure $p$ observe the equation of state $p + \rho = 0$ (as for dark energy), with no pressures on $\theta-$ and $\phi-$ directions. However, the angular components of the viscous part of the stress tensor are nonvanishing and equals the energy density of the fluid.