Gravitational Collapse in Generalized Vaidya Space-Time for Lovelock Gravity Theory

TL;DR

This paper investigates gravitational collapse in generalized Vaidya spacetime within Lovelock gravity theories, analyzing how parameters influence the formation of black holes or naked singularities across different dimensions.

Contribution

It provides a comparative analysis of singularity formation in Gauss-Bonnet, dimensionally continued, and pure Lovelock gravity theories, highlighting parameter effects and dimensional dependencies.

Findings

Naked singularities are more likely in higher dimensions in Gauss-Bonnet gravity.

Odd dimensions favor naked singularities in dimensionally continued Lovelock gravity.

Pure Lovelock gravity always results in black hole formation regardless of parameters.

Abstract

In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in $(n+2)$-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.