Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

TL;DR

This paper studies the gravitational collapse of dust clouds in higher-dimensional Einstein-Gauss-Bonnet gravity, revealing how the final fate varies with dimension and initial conditions, including the formation of naked singularities and violations of cosmic censorship.

Contribution

It generalizes the Misner-Sharp formalism to higher dimensions in Einstein-Gauss-Bonnet gravity and analyzes the collapse outcomes, highlighting differences between five and higher dimensions.

Findings

Bounce occurs in plus-branch solutions for n ≥ 6, preventing singularities.

Naked singularities can form in certain dimensions, violating cosmic censorship.

Collapse behavior and singularity nature depend strongly on the spacetime dimension.

Abstract

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$ with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with $n=5$ and $n \ge 6$. There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of $n=5$ must be naked. In the minus-branch solution, naked singularities are massless for $n \ge 6$, while massive naked singularities are possible for $n=5$. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for $n \ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge 10$ and for $n=9$ depending on the parameters in the initial data, while a naked singularity is always formed for $5 \le n \le 8$. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.