Gravitational Collapse with a Cosmological Constant

TL;DR

This paper analyzes how a positive cosmological constant influences spherical gravitational collapse, constructing exact solutions like the OSdS spacetime, and exploring phenomena such as bouncing or hovering dust balls due to cosmic repulsion.

Contribution

It generalizes the Oppenheimer-Snyder solution to include a cosmological constant and examines new collapse behaviors like bouncing and equilibrium states.

Findings

Cosmological constant can delay initial collapse but becomes less influential later.

Constructed exact OSdS spacetime incorporating a positive cosmological constant.

Identified conditions for bouncing and hovering dust configurations.

Abstract

We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.