Pure Gauss-Bonnet NUT Black Hole Solution: I

TL;DR

This paper presents a new exact solution for a six-dimensional NUT black hole in pure Gauss-Bonnet gravity with a product topology horizon, analyzing its structure and physical viability.

Contribution

It introduces a novel six-dimensional NUT black hole solution in pure Gauss-Bonnet gravity with detailed horizon and singularity analysis, and establishes topological constraints for NUT spacetimes.

Findings

New exact six-dimensional NUT black hole solution.

Product topology of horizons in higher-dimensional NUT black holes.

Parameter window for physical viability of the solution.

Abstract

We find a new exact $\Lambda$-vacuum solution in pure Gauss-Bonnet gravity with NUT charge in six dimension with horizon having product topology $S^{(2)} \times S^{(2)}$. We also discuss its horizon and singularity structure, and consequently arrive at a parameter window for its physical viability. It should be noted that all NUT black hole solutions in higher dimensions have product, instead of spherical, topology. We prove, in general, that it is because of the radial symmetry of the NUT spacetime; i.e. in higher dimensions NUT spacetime cannot maintain radial symmetry unless horizon has $S^{(2)}$ or its product topology. On the way we also prove a general result for spherical symmetry that when null energy condition is satisfied, one has then only to solve a first order equation to get a vacuum or $\Lambda$-vacuum solution.