Conformal time dependent Painleve-Gullstrand spacetime

TL;DR

This paper investigates the properties of anisotropic fluids in an expanding universe using Painleve-Gullstrand coordinates, revealing unique behaviors of heat flux, pressures, and energy density near black holes and singularities.

Contribution

It introduces a novel analysis of anisotropic fluids in a cosmological setting within Painleve-Gullstrand coordinates, highlighting their unique stress-energy characteristics.

Findings

Heat flux of the cosmological fluid vanishes despite non-zero stress tensor components.

Pressures and energy density are regular at the black hole horizon but diverge at the singularity.

Pressures and energy density change sign at specific radial values.

Abstract

The properties of an anisotropic fluid outside a star or a black hole embedded in an expanding universe are investigated. One finds that, in Painleve-Gullstrand coordinates, the heat flux of the cosmological fluid vanishes, in spite of the nonzero value of a non-diagonal component of the stress tensor. The pressures and energy density of the fluid are regular at $r = 2m$, divergent at $r = 0$ and change sign at certain values of their arguments.