A metric for gravitational collapse of dust around a Schwarzschild black hole

TL;DR

This paper develops a new class of metrics describing the gravitational collapse of dust around a Schwarzschild black hole, revealing complex pressure behaviors outside the horizon.

Contribution

It introduces a novel metric framework for dust collapse near black holes, encompassing previous models as special cases and analyzing pressure variations.

Findings

Radial and tangential pressures can be positive or negative outside the horizon.

The derived metrics include dust collapse as a special case.

The model provides insights into the dynamics of dust near black holes.

Abstract

We consider the problem of gravitational collapse of a fluid under the effect of a Schwarzschild black hole (e.g. a primordial one) that suddenly forms inside the fluid. We assume the fluid initially be a uniform dust. Starting from this configuration we obtain a class of metrics under some assumptions. We find that the metric we obtain includes the dust collapse as a subcase. After discussing some basic properties of the solution, we discuss the case of dust collapse in more detail. We find that the radial and tangential pressures outside the horizon may take positive or negative values depending on the values of the parameters.