Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant

TL;DR

This paper demonstrates that Gauss-Bonnet gravity can produce asymptotically (anti-)de Sitter and flat solutions without a cosmological constant, revealing new black hole and topological solutions with unique mass properties in five dimensions.

Contribution

It introduces novel static, rotating, and magnetic solutions in Gauss-Bonnet gravity without a cosmological constant, highlighting unique mass characteristics in five dimensions.

Findings

Existence of asymptotically dS, AdS, and flat solutions without cosmological constant.

Discovery of black hole, topological black hole, and naked singularity solutions.

Geometrical mass differs from Einstein gravity in five dimensions.

Abstract

In this paper we show that one can have asymptotically de Sitter (dS), anti-de Sitter (AdS) and flat solutions in Gauss-Bonnet gravity without any need to a cosmological constant term in field equations. First, we introduce static solutions whose 3-surfaces at fixed $r$ and $t$ have constant positive ($k=1$), negative ($k=-1$), or zero ($k=0$) curvature. We show that for $k=\pm1$, one can have asymptotically dS, AdS and flat spacetimes, while for the case of $k=0$, one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. We also find that the geometrical mass of these 5-dimensional spacetimes is $m+2\alpha | k| $, which is different from the geometrical mass, $m $, of the solutions of Einstein gravity. This feature occurs only for the 5-dimensional solutions, and is not repeated for the solutions of Gauss-Bonnet gravity in higher dimensions. We also add angular momentum to the static solutions with $k=0$, and introduce the asymptotically AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, we introduce a class of solutions which yields an asymptotically AdS spacetime with a longitudinal magnetic field which presents a naked singularity, and generalize it to the case of magnetic rotating solutions with two rotation parameters.