Scalar hairy black holes with an inverted Mexican-hat potential
Xiao Yan Chew, Kok-Geng Lim
Abstract
We numerically construct the asymptotically flat solutions of hairy black holes supported by a symmetric inverted Mexican hat potential with a local minimum and two degenerate global maxima of a real scalar field that contains a quartic self-interaction term. The solutions of hairy black holes emerge from the Schwarzschild black hole when the nontrivial scalar field exists outside the event horizon. Therefore, we perform a comprehensive study on the properties of the hairy black holes such as the area of ehorizon, the Hawking temperature, the innermost stable circular orbit, the photon sphere, etc. We also numerically study their linear stability in the mode analysis, hence finding that they are unstable against the linear perturbation.