Spinning exact solutions with Sasakian structure in Gauss-Bonnet Maxwell gravity

TL;DR

This paper presents new exact, stationary, non-static solutions in higher-dimensional Einstein Gauss-Bonnet gravity coupled with Maxwell fields, exhibiting Sasakian structure and asymptotic AdS behavior, and explores their relation to known rotating solutions.

Contribution

It introduces a novel class of solutions with Sasakian structure in higher-dimensional Gauss-Bonnet-Maxwell gravity, expanding the understanding of such spacetimes.

Findings

Solutions are stationary, non-static, and asymptotically AdS.

The metric exhibits Sasakian structure, a unique geometric property.

Confirmed the physical validity via finite angular momentum evaluation.

Abstract

We obtain new exact solutions in Einstein Gauss-Bonnet gravity of every odd dimension higher than three. These new spacetimes are stationary but non-static, coupled with the Maxwell field, and asymptotic AdS at least locally. In order to investigate such new solutions, we adopt the characteristic ansatz for the metric form. It is presented that the local expression of our metric possesses some interesting properties, in which the most peculiar one is what is called Sasakian structure. Somewhat intricate relationship is unveiled between our solution and the already-known rotating solution which has been only one so far in that purely gravitational theory. We confirm the validity of the rotating spacetime with the evaluation of the finite angular momentum.