Abstract
It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of 2-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss–Bonnet Lambda -vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at r ne 0.
Highlights
NUT spacetime is the most enigmatic solution of the Einstein vacuum equation
It turns out that all higher dimensional NUT solutions do not have spherical topology but instead have product of 2-spheres [12,13,14,15,16,17]. This is because spherical topology in dimension, D − 2 > 2 is not compatible with radial symmetry, which is a primary property of NUT spacetime [18]
Note that the occurrence of non-centric singularity is due to product topology which is present even when absence of NUT charge [22]
Summary
NUT spacetime is the most enigmatic solution of the Einstein vacuum equation. It is the most general radially symmetric solution when asymptotic flatness condition is lifted off. Note that the occurrence of non-centric singularity is due to product topology which is present even when absence of NUT charge [22]. By choosing the topology of product of two spheres, S(2)× S(2), we have obtained a new solution [18] of pure GB vacuum equation for a black hole with NUT charge and it is given by the metric, ds2 = −ρ2 dt + P1dφ1 + P2dφ2
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