Probing pure Lovelock gravity by Nariai and Bertotti-Robinson solutions

TL;DR

This paper investigates the properties of Nariai and Bertotti-Robinson solutions within pure Lovelock gravity, demonstrating that their characterization remains consistent in higher dimensions and exploring their behavior in Einstein-Gauss-Bonnet gravity.

Contribution

It extends the understanding of product spacetime solutions to pure Lovelock gravity in higher dimensions, confirming their characterization and analyzing their behavior in Einstein-Gauss-Bonnet gravity.

Findings

Nariai and Bertotti-Robinson solutions retain their characterization in pure Lovelock gravity.

The solutions are valid in dimensions d=2N+2 for pure Lovelock gravity.

Analysis includes Einstein-Gauss-Bonnet gravity as a special case.

Abstract

The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $\Lambda$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventional setting of Einstein-Gauss-Bonnet gravity.