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Charged scalar-tensor solitons and black holes with (approximate) anti-de Sitter asymptotics. (English) Zbl 1409.83087
Summary: We discuss charged and static solutions in a shift-symmetric scalar-tensor gravity model including a negative cosmological constant. The solutions are only approximately Anti-de Sitter (AdS) asymptotically. While spherically symmetric black holes with scalar-tensor hair do exist in our model, the uncharged spherically symmetric scalar-tensor solitons constructed recently cannot be generalised to include charge. We point out that this is due to the divergence of the electric monopole at the origin of the coordinate system, while higher order multipoles are well-behaved. We also demonstrate that black holes with scalar hair exist only for horizon value larger than that of the corresponding extremal Reissner-Nordström-AdS (RNAdS) solution, i.e. that we cannot construct solutions with arbitrarily small horizon radius. We demonstrate that for fixed \(Q\) a horizon radius exists at which the specific heat \(C_Q\) diverges – signalling a transition from thermodynamically unstable to stable black holes. In contrast to the RNAdS case, however, we have only been able to construct a stable phase of large horizon black holes, while a stable phase of small horizon black holes does not (seem to) exist.

83C57 Black holes
83C15 Exact solutions to problems in general relativity and gravitational theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C22 Einstein-Maxwell equations
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