Asymptotically Flat Radiating Solutions in Third Order Lovelock Gravity

TL;DR

This paper derives an exact spherically symmetric solution in third order Lovelock gravity describing gravitational collapse, revealing that the third order term influences the formation and strength of naked singularities in higher dimensions.

Contribution

It provides the first explicit solution for radiating collapse in third order Lovelock gravity and analyzes the impact on singularity strength across dimensions.

Findings

Naked singularities are inevitably formed during collapse.

The third order Lovelock term weakens the strength of curvature singularities.

Singularity strength varies with the number of dimensions, being different for n=7 and n≥8.

Abstract

In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in $n$ dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat depending on the choice of the cosmological constant. Using the asymptotically flat solution for $n \geq 7$ with a power-law form of the mass as a function of the null coordinate, 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 whose strength is different for the $n = 7$ and $n \geq 8$ cases. In the $n=7$ case, the limiting focusing condition for the strength of curvature singularity is satisfied. But for $n \geq 8$, the strength of curvature singularity depends on the rate of increase of mass of the spacetime. These considerations show that the third order Lovelock term weakens the strength of the curvature singularity.