ﻻ يوجد ملخص باللغة العربية
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 was used to show the non-existence of unstable mode. However, in some cases, it is hard to find an appropriate deformation function analytically because the only way known so far to find it is a try-and-error approach. In this paper, we show that it is easy to find a regular deformation function by numerically solving the differential equation such that the deformed potential vanishes everywhere, when the spacetime is stable. Even if the spacetime is almost marginally stable, our method still works. We also discuss a simple toy model which can be solved analytically, and show the condition for the non-existence of a bound state is the same as that for the existence of a regular solution for the differential equation in our method. From these results, we conjecture that our criteria is also a necessary condition.
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 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
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
We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of R
We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential, and a toy model for the time-dependent evol