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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 method works well, general discussion is not given yet explicitly. In this paper, we show the existence of a regular $S$-deformation when a black hole spacetime is stable under some reasonable assumptions. This $S$-deformation is constructed from a solution of a differential equation. We also show that the boundary condition for the differential equation which corresponds to a regular $S$-deformation has a one-parameter degree of freedom with a finite range. This is the reason why any fine-tune technique is not needed to find $S$-deformation numerically.
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
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
The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall for gravitat
In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calc
We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a si