Black hole quasinormal modes in a scalar-tensor theory with field derivative coupling to the Einstein tensor

Abstract

We investigate the quasinormal modes of a test massless, minimally coupled scalar field on a static and spherically symmetric black hole in the scalar-tensor theory with field derivative coupling to the Einstein tensor, which is a part of the Horndeski theory with the shift symmetry. In our solution, the spacetime is asymptotically AdS (anti-de Sitter), where the effective AdS curvature scale is determined solely by the derivative coupling constant. The metric approaches the AdS spacetime in the asymptotic infinity limit and precisely recovers the Schwarzschild-AdS solution in general relativity if the coupling constant is tuned to the inverse of the cosmological constant. We numerically find the lowest lying quasinormal frequency for the perturbation about a test massless, minimally coupled scalar field. The quasinormal frequency agrees with that of the Schwarzschild-AdS solution for the tuned case. For other parameters, in the large black hole limit, as the metric coincides with that of the Schwarzschild-AdS black hole, the quasinormal frequency almost agrees with that of the Schwarzschild-AdS black hole and is insensitive to the value of the cosmological constant. On the other hand, for a small back hole the real part of the quasinormal frequency decreases as the absolute value of the cosmological constant increases.

10 pages, 4 figures, comments and references added, typos fixed, matched to the version published in GRG

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Cited by in corpus (11)

• Gravitational perturbations of non-singular black holes in conformal gravity
• Echoes of Compact Objects in Scalar-Tensor Theories of Gravity
• Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field
• Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
• Black hole perturbations in Maxwell-Horndeski theories
• Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor
• Self Tuning Scalar Fields in Spherically Symmetric Spacetimes
• Quasi-normal modes of black holes in scalar-tensor theories with non-minimal derivative couplings
• Stealth black holes in shift symmetric kinetic gravity braiding
• Instability of Reissner-Nordström-AdS black hole under perturbations of a scalar field coupled to Einstein tensor
• Spherically symmetric, static black holes with scalar hair, and naked singularities in nonminimally coupled k-essence