Probing pure Lovelock gravity by Nariai and Bertotti-Robinson solutions

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.

Title changed, contents reordered, changes in the introduction to clarify some points

References in corpus (4)

• The Lovelock gravity in the critical spacetime dimension
• On the static Lovelock black holes
• Lovelock black holes with maximally symmetric horizons
• Thermodynamical universality of the Lovelock black holes

Cited by in corpus (7)

• Lanczos-Lovelock gravity from a thermodynamic perspective
• Universality of isothermal fluid spheres in Lovelock gravity
• Symmetry Breaking Vacua in Lovelock Gravity
• Thin-shell Wormholes with Ordinary Matter in Pure Gauss-Bonnet Gravity
• Lovelock vacua with a recurrent null vector field
• Bertotti-Robinson solutions in five--dimensional quadratic gravity
• Euler-Lagrange formulas for pseudo-Kaehler manifolds