Gravitational Collapse in Massive Gravity on de Sitter Spacetime

TL;DR

This paper investigates gravitational collapse in ghost-free massive gravity on de Sitter spacetime, revealing conditions under which collapse occurs, properties of apparent horizons, and implications for static black hole solutions.

Contribution

It provides the first analysis of gravitational collapse in massive gravity on de Sitter space, identifying conditions for collapse and showing that static black hole solutions are unlikely.

Findings

Collapse does not occur for all parameters.

Apparent horizon location is derived during collapse.

Collapsing solutions cannot match static vacuum solutions.

Abstract

We analyze the evolution of a homogenous and pressureless ball of dust (or "star") in ghost-free massive gravity on de Sitter spacetime. We find that gravitational collapse does not take place for all parameters of the massive gravity theory. For parameters where it does occur, we find the expression for the location of the apparent horizon where it crosses the surface of the star, indicating the location of the apparent horizon of the vacuum solution at that moment. We determine the Ricci curvature at the boundary of the star and extract the finite correction to the curvature of the apparent horizon due to the graviton mass. Finally, we argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.