http://arxiv.org/abs/2201.09687
We study linear perturbations about static and spherically symmetric black holes with a time-independent background scalar field in shift-symmetric Horndeski theories, whose Lagrangian is characterized by coupling functions depending only on the kinetic term of the scalar field $X$. We clarify conditions for the absence of ghosts and Laplacian instabilities along the radial and angular directions in both odd- and even-parity perturbations. For reflection-symmetric theories described by a k-essence Lagrangian and a nonminimal derivative coupling with the Ricci scalar, we show that black holes endowed with nontrivial scalar hair are unstable around the horizon in general. This includes non-asymptotically-flat black holes known to exist when the nonminimal derivative coupling to the Ricci scalar is a linear function of $X$. We also investigate several black hole solutions in non-reflection-symmetric theories. For cubic Galileons with the Einstein-Hilbert term, there exists a non-asymptotically-flat hairy black hole with no ghosts/Laplacian instabilities. Also, for the scalar field linearly coupled to the Gauss-Bonnet term, asymptotically-flat black hole solutions constructed perturbatively with respect to a small coupling are free of ghosts/Laplacian instabilities.
M. Minamitsuji, K. Takahashi and S. Tsujikawa
Tue, 25 Jan 22
66/78
Comments: 21 pages, 1 figure, 1 table