Matter without matter: novel Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

TL;DR

This paper explores novel solutions in Einstein-Gauss-Bonnet gravity on higher-dimensional Kaluza-Klein spacetimes, revealing unique gravitational phenomena and solutions specific to four-dimensional spacetime, including black holes and Taub-NUT analogues.

Contribution

It introduces new exact solutions in Einstein-Gauss-Bonnet gravity on Kaluza-Klein spacetimes, highlighting the special role of four-dimensional spacetime in gravitational creation phenomena.

Findings

Existence of a new static black-hole solution in higher-dimensional Einstein-Gauss-Bonnet gravity.

Gravitational creation of Maxwell fields occurs only in four-dimensional spacetime.

New exact solutions including analogues in Taub-NUT spacetime on four-dimensional manifolds.

Abstract

We consider Einstein-Gauss-Bonnet gravity in $n(\ge 6)$-dimensional Kaluza-Klein spacetime ${\ma M}^{4} \times {\ma K}^{n-4}$, where ${\ma K}^{n-4}$ is the Einstein space with negative curvature. In the case where ${\ma K}^{n-4}$ is the space of negative constant curvature, we have recently obtained a new static black-hole solution (Phys. Rev. D {\bf 74}, 021501(R) (2006), hep-th/0605031) which is a pure gravitational creation including Maxwell field in four-dimensional vacuum spacetime. The solution has been generalized to make it radially radiate null radiation representing gravitational creation of charged null dust. The same class of solutions though exists in spacetime ${\ma M}^{d} \times {\ma K}^{n-d}$ for $d=3,4$, however the gravitational creation of the Maxwell field is achieved only for $d=4$. Also, Gauss-Bonnet effect could be brought down to ${\ma M}^d$ only for $d=4$. Further some new exact solutions are obtained including its analogue in Taub-NUT spacetime on ${\ma M}^4$ for $d=4$.