Exact solutions for spherically gravitational collapse around a black hole: the effect of tangential pressure

TL;DR

This paper derives exact solutions for spherically symmetric gravitational collapse around a black hole considering tangential pressure, revealing three possible outcomes influenced by pressure and mass parameters.

Contribution

It provides new exact solutions for gravitational collapse with tangential pressure, showing how pressure affects the collapse dynamics and end states.

Findings

Positive tangential pressure leads to collapse, expansion, or unstable static solutions.

Shells with zero or negative pressure always collapse into the black hole.

All collapsing shells cross the event horizon, not accumulate outside it.

Abstract

Spherically gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact solutions have three qualitatively different endings. For positive tangential pressure, the shell around a black hole may eventually collapse onto the black hole, or expand to infinity, or have a static but unstable solution, depending on the combination of black hole mass, mass of the shell and the pressure parameter. For vanishing or negative pressure, the shell will collapse onto the black hole. For all eventually collapsing solutions, the shell will cross the event horizon, instead of accumulating outside the event horizon, even if clocked by a distant stationary observer.