Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
arXiv:1904.03554 · doi:10.1103/PhysRevD.100.024041
Abstract
We study static spherically symmetric black hole solutions with a linearly time-dependent scalar field and discuss their linear stability in the shift- and reflection-symmetric subclass of quadratic degenerate higher-order scalar-tensor (DHOST) theories. We present the explicit forms of the reduced system of background field equations for a generic theory within this subclass. Using the reduced equations of motion, we show that in several cases the solution is forced to be of the Schwarzschild or Schwarzschild-(anti-)de Sitter form. We consider odd-parity perturbations around general static spherically symmetric black hole solutions, and derive the concise criteria for the black holes to be stable. Our analysis also covers the case with a static or constant profile of the scalar field.
arXiv comment18 pages; matches published version
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