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We propose a simple method to prove the linear mode stability of a black hole when the perturbed field equations take the form of a system of coupled Schrodinger equations. The linear mode stability of the spacetime is guaranteed by the existence of an appropriate $S$-deformation. Such an $S$-deformation is related to the Riccati transformation of a solution to the Schrodinger system with zero energy. We apply this formalism to some examples and numerically study their stability.
The $S$-deformation method is a useful way to show the linear mode stability of a black hole when the perturbed field equation takes the form of the Schrodinger equation. While previous works where many explicit examples are studied suggest that this
We study a sufficient condition to prove the stability of a black hole when the master equation for linear perturbation takes the form of the Schrodinger equation. If the potential contains a small negative region, usually, the $S$-deformation method
Black holes in $f(R)$-gravity are known to be unstable, especially the rotating ones. In particular, an instability develops that looks like the classical black hole bomb mechanism: the linearized modified Einstein equations are characterized by an e
In the present paper the repulsion of two extreme Kerr black holes arising from their spin-spin interaction is analyzed within the framework of special subfamilies of the well-known Kinnersley-Chitre solution. The binary configurations of both equal
In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order