Effects of Gauss-Bonnet term on the final fate of gravitational collapse

TL;DR

This paper explores how the Gauss-Bonnet term influences gravitational collapse in higher dimensions, revealing the inevitable formation of naked singularities with properties differing from general relativity, depending on the number of dimensions.

Contribution

It provides a new spherically symmetric solution in Gauss-Bonnet gravity for higher dimensions and analyzes the nature of resulting naked singularities during collapse.

Findings

Naked singularities form inevitably in the model.

Properties of singularities differ between 5 and ≥6 dimensions.

Naked singularities are weaker than in general relativity.

Abstract

We obtain a general spherically symmetric solution of a null dust fluid in $n (\geq 4)$-dimensions in Gauss-Bonnet gravity. This solution is a generalization of the $n$-dimensional Vaidya-(anti)de Sitter solution in general relativity. For $n=4$, the Gauss-Bonnet term in the action does not contribute to the field equations, so that the solution coincides with the Vaidya-(anti)de Sitter solution. Using the solution for $n \ge 5$ with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between $n=5$ and $n \ge 6$. In the $n \ge 6$ case, a massless ingoing null naked singularity is formed, while in the $n=5$ case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime.