Dust collapse and horizon formation in Quadratic Gravity

TL;DR

This paper investigates dust star collapse in Quadratic Gravity, revealing horizon formation and faster singularity development compared to General Relativity, with more restrictive junction conditions.

Contribution

First analysis of spherically symmetric dust collapse in Quadratic Gravity showing horizon formation and modified dynamics due to curvature-squared terms.

Findings

Collapse results in horizon formation, not horizonless spacetime.

Curvature-squared terms accelerate singularity formation.

Junction conditions are more restrictive than in GR.

Abstract

Quadratic Gravity supplements the Einstein-Hilbert action by terms quadratic in the spacetime curvature. This leads to a rich phase space of static, compact gravitating objects including the Schwarzschild black hole, wormholes, and naked singularities. For the first time, we study the collapse of a spherically symmetric star with uniform dust density in this setting. We assume that the interior geometry respects the symmetries of the matter configuration, i.e., homogeneity and isotropy, thus it is insensitive to the Weyl-squared term and the interior dynamics is fully determined by $R$ and $R^2$. As our main result, we find that the collapse leads to the formation of a horizon, implying that the endpoint of a uniform dust collapse with a homogeneous and isotropic interior is not a horizonless spacetime. We also show that the curvature-squared contribution is responsible for making the collapse into a singularity faster than the standard Oppenheimer-Snyder scenario. Furthermore, the junction conditions connecting spacetime inside and outside the matter distribution are found to be significantly more constraining than their counterparts in General Relativity and we discuss key properties of any exterior solution matching to the spacetime inside the collapsing star. Finally, we comment on the potentially non-generic behavior entailed by our assumptions.