Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory

Abstract

The Schwarzschild-de Sitter solution in the Einstein theory with a positive cosmological constant $\Lambda =m^2/\alpha$ becomes an exact solution to the dRGT non-linear massive gravity theory with the mass parameter $m$ when the theory parameters $\alpha$ and $\beta$ satisfy the relation $\beta ={\alpha }^2$. We study the perturbative behaviour of this black hole solution in the non-linear dRGT theory with $\beta ={\alpha }^2$. We find that the linear perturbation equations become identical to those for the vacuum Einstein theory when they are expressed in terms of the gauge-invariant variables. This implies that this black hole is stable in the dRGT theory as far as the spacetime structure is concerned in contrast to the case of the bi-Schwarzschild solution in the bi-metric theory. However, we have also found a pathological feature that the general solution to the perturbation equations contain a single arbitrary function of spacetime coordinates. This implies a degeneracy of dynamics in the Stückelberg field sector at the linear perturbation level in this background. Physical significance of this degenercy depends on how the Stückelberg fields couple observable fields.

Minor corrections

References in corpus (7)

• Resummation of Massive Gravity
• Screening of cosmological constant in non-local gravity
• Can a non-local model of gravity reproduce Dark Matter effects in agreement with MOND?
• Perturbations and Stability of Higher-Dimensional Black Holes
• Modified Gravitational Theory as an Alternative to Dark Energy and Dark Matter
• General Massive Spin-2 on de Sitter Background
• Analytic formulae for the off-center CMB anisotropy in a general spherically symmetric universe

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