1210.1109 (Naresh Dadhich et al.)

On universality of the pure Lovelock gravity for the generalized Nariai
and Bertotti-Robinson solutions    [PDF]

Naresh Dadhich, Josep M. Pons

The product spacetimes of constant curvature describe in the Einstein gravity, which is linear in the Riemann curvature, the Nariai metric which is a solution of the $\Lambda$-vacuum when the two curvatures are equal, $k_1=k_2$, while it is the Bertotti-Robinson metric describing the uniform electric field when the curvatures are equal and opposite, $k_1=-k_2$. We prove that this is indeed true in general for the pure Lovelock gravity of any order $N$, where the action involves only the $N$th order term in the Lovelock Lagrangian, in $d=2N+2$ dimension. We thus establish universality of these spacetimes for the pure Lovelock gravity. Besides we also discuss some other interesting aspects including some new pure Lovelock vacuum solutions of the type $(dS/AdS)_2\times E^{d-2}$ and $ M^2 \times K^{d-2}$ where $M, E$ and $K$ refer respectively to Minkowski, Euclidean and space of constant curvature. We also consider these product spacetimes in full generality for the Einstein-Guass-Bonnet gravity.

View original: http://arxiv.org/abs/1210.1109