Rotating stealth black holes with a cohomogeneity metric

Olaf Baake; Mokhtar Hassaine

doi:10.1140/epjc/s10052-021-09449-2

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 642
https://doi.org/10.1140/epjc/s10052-021-09449-2

Regular Article - Theoretical Physics

Rotating stealth black holes with a cohomogeneity $- 1$ metric

Olaf Baake¹^,2^a and Mokhtar Hassaine¹

¹ Instituto de Matemática (INSTMAT), Universidad de Talca, Casilla 747, 3460000, Talca, Chile
² Centro de Estudios Cientificos (CECs), Av. Arturo Part 514, 5090000, Valdivia, Chile

^a olaf.baake@inst-mat.utalca.cl

Received: 17 May 2021
Accepted: 12 July 2021
Published online: 22 July 2021

Abstract

In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers–Perry spacetime with equal momenta and the scalar field is identified with the Hamilton–Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers–Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers–Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity $- 1$ $$-1$$ character of the Myers–Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity $- 1$ $$-1$$ metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr+-de Sitter case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory.

© The Author(s) 2021

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