We obtain a class of asymptotic flat or (anti)–de Sitter [(A)dS] hairy black holes in $D$-dimensional Einstein gravity coupled to a scalar with a certain scalar potential. For a given mass, the theory admits both the Schwarzschild-Tangherlini and the hairy black holes with different temperature and entropy, but satisfying the same first law of thermodynamics. For some appropriate choice of parameters, the scalar potential can be expressed in terms of a superpotential, and it can arise in gauged supergravities. In this case, the solutions develop a naked curvature singularity and become the spherical domain walls. Uplifting the solutions to $D=11$ or 10, we obtain solutions that can be viewed as spherical M-branes or D3-branes. We also add electric charges to these hairy black holes. All these solutions contain no scalar charges in that the first law of thermodynamics is unmodified. We also try to construct new AdS black holes carrying scalar charges, with some moderate success in that the charges are pre-fixed in the theory instead of being some continuous integration constants.

• Received 30 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.044014