Scalar hairy black holes in general dimensions

Abstract

We obtain a class of asymptotic flat or (A)dS hairy black holes in D-dimensional Einstein gravity coupled to a scalar with 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 super-potential 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 are 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.

Exact collapse solutions in D = 4, N $$ \mathcal{N} $$ = 4 gauged supergravity and their generalizations

“…It was later re-derived for the construction of neutral or charged scalar-hairy black holes [16][17][18][19], and also appeared in the time-dependent scalar-hairy black hole in [10]. Adopting the same ansatz and following the same procedure as in section 2, we find that the theory admits the following time-dependent solution:…”

Hairy planar black holes in higher dimensions

“…Note added: after our work was posted in the arXiv, the same self-interaction was studied in the context of spherically symmetric solutions and its embedding in ten and eleven dimensions [16].…”

Strategy to construct exact solutions in Einstein-scalar gravities

“…However, as there is too much freedom in constructing a scalar potential without breaking any essential symmetry, starting from some arbitrary scalar potential, the possibility to find an exact solution could be almost null. Hence it is not surprising that there is not much progress [9,10] in constructing exact solutions for a long time until recently [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], people begin to think in a reverse way, which is trying to give a proper Ansatz for the scalar field first then deriving the corresponding Lagrangian (or scalar potential) through the EOMs at last.…”