The spherical perfect fluid collapse with pressure in the cosmological background

TL;DR

This paper models a spherically symmetric perfect fluid structure with pressure in a cosmological setting, analyzing black hole evolution and horizon properties using numerical integration of Einstein's equations.

Contribution

It introduces a numerical algorithm to study pressure effects in cosmological black holes within a Lemaître framework, revealing complex horizon and mass evolution behaviors.

Findings

Black hole decoupling from the universe expansion

Structure of the apparent horizon in the model

Decreasing mass infall to the black hole

Abstract

We have constructed a spherically symmetric structure model in a cosmological background filled with perfect fluid with non-vanishing pressure and studied its quasi-local characteristics. This is done by using the Lema\^{i}tre solution of the Einstein equations and suggesting an algorithm to integrate it numerically. The result shows intriguing effects of the pressure inside the structure. The evolution of the central black hole within the FRW universe, its decoupling from the expanding parts of the model, the structure of its space-like apparent horizon, the limiting case of the dynamical horizon tending to a slowly evolving horizon, and the decreasing mass in-fall to the black hole is also studied. The quasi-local features of this cosmological black hole may not be inferred from the weak field approximation although the gravity outside the structure is very weak.