Abstract
A class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented. These spacetimes are asymptotically locally anti-de Sitter manifolds and have a Ricci-flat event horizon hiding a curvature singularity at the origin. The scalar field is real and regular everywhere and its effective mass, coming from the nonminimal coupling with the scalar curvature, saturates the Breitenlohner-Freedman bound for the corresponding spacetime dimension. The rotating black hole is obtained by applying an improper coordinate transformation to the static one. Although both spacetimes are locally equivalent, they are globally different, as it is confirmed by the nonvanishing angular momentum of the rotating black hole. It is found that the mass is bounded from below by the angular momentum in agreement with the existence of an event horizon. The thermodynamical analysis is carried out in the grand canonical ensemble. The first law is satisfied and a Smarr formula is exhibited. The thermodynamical local stability of the rotating hairy black holes is established from their Gibbs free energy. However, the global stability analysis establishes that the vacuum spacetime is always preferred over the hairy black hole. Thus, the hairy black hole is likely to decay into the vacuum one for any temperature.
Highlights
In the last years a number of static black holes dressed with scalar field have been found in different dimensions
For a self-interacting real scalar field nonminimally coupled to the Ricci invariant, exact black hole solutions have been found in three [1,2,3,4], four [5,6,7,8,9,10,11,12,13,14,15,16] and even in higher dimensions [17,18,19,20,21,22], including in some cases the presence of other matter fields
Four-dimensional black holes endowed with angular momentum in the presence of matter fields have a crucial role in astrophysics
Summary
In the last years a number of static black holes dressed with scalar field have been found in different dimensions These black holes circumvent the well-known no-hair conjecture by violating some of its assumptions, for instance, by introducing a cosmological constant, considering a suitable potential or allowing nonminimal couplings. A crucial point in the construction of such a class of black holes is based on the fact that an improper coordinate transformation acting on a static metric could generate a stationary one with nonvanishing angular momentum. This nontrivial effect was shown by Stachel in [30], and the physical interpretation of the parameters of this improper local transformation was studied in [31].
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