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arXiv · 1312.7736

Lifshitz black holes with a time-dependent scalar field in Horndeski theory

Moises Bravo-Gaete·Mokhtar Hassaine
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Abstract

In arbitrary dimensions, we consider a particular Horndeski action given by the Einstein-Hilbert Lagrangian with a cosmological constant term, while the source part is described by a real scalar field with its usual kinetic term together with a nonminimal kinetic coupling. In order to evade the no-hair theorem, we look for solutions where the radial component of the conserved current vanishes identically. Under this hypothesis, we prove that this model can not accommodate Lifshitz solutions with a radial scalar field. This problem is finally circumvented by turning on the time dependence of the scalar field, and we obtain a Lifshitz black hole solution with a fixed value of the dynamical exponent z=1/3. The same metric is also shown to satisfy the field equations arising only from the variation of the matter source.

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Moises Bravo-Gaete, Mokhtar Hassaine. 2014-04-21. Lifshitz black holes with a time-dependent scalar field in Horndeski theory. https://doi.org/10.1103/physrevd.89.104028

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