Compact objects in pure Lovelock theory

TL;DR

This paper explores static fluid interiors of compact objects in pure Lovelock gravity, revealing dimensional similarities and differences, and introduces a Lovelock analogue of the Finch-Skea model.

Contribution

It establishes dimensional similarity in solutions for pure Lovelock gravity and introduces a new analogue of the Finch-Skea model within this framework.

Findings

No finite radius bound distributions in odd critical dimensions.

All solutions exhibit similar behavior in even critical dimensions.

Comparison of star solutions in Einstein and Gauss-Bonnet theories.

Abstract

For static fluid interiors of compact objects in pure Lovelock gravity (involving ony one $N$th order term in the equation) we establish similarity in solutions for the critical odd and even $d=2N+1, 2N+2$ dimensions. It turns out that in critical odd $d=2N+1$ dimensions, there can exist no bound distribution with a finite radius, while in critical even $d=2N+2$ dimensions, all solutions have similar behavior. For exhibition of similarity we would compare star solutions for $N =1, 2$ in $d=4$ Einstein and $d=6$ in Gauss-Bonnet theory respectively. We also obtain the pure Lovelock analogue of the Finch-Skea model.