Quasinormal modes and echo effect of a cylindrical anti-de Sitter black hole spacetime with a thin shell

This paper investigates the quasinormal mode (QNM) vibrations of a rotating cylindrical black hole (or black string) spacetime that is surrounded by a thin shell rotating synchronously with the black string's axis. The existence of the thin shell leads to a piecewise metric of the black hole spacetime beyond the horizon, which is divided into two stationary spacetime parts by the radius of the thin shell. As a result, the potential function Vor thorn of the QNM equation is also discontinuous. To solve the QNM equation with the discontinuous potential function, we propose two methods, the matrix method and the generalized Horowitz-Hubeny method. We find that the influence of the thin shell can reduce the QNM frequency of the black string while alleviating their amplitude decay rate. Our suggested method can be easily applied to other QNM calculations of black hole spacetime with discontinuous potential function, thus facilitating investigations into more intricate and realistic black hole spacetimes, such as those with accretion disks. Additionally, the finite difference method is employed to investigate the spacetime too. This analysis discloses a substantial gap in the potential function when the thin shell's mass and charge achieve sufficiently high values, resulting in the outer spacetime nearing gravitational collapse and extreme black hole scenarios. Within this gap, the QNM wave displays oscillations, producing an echo effect. Moreover, it is established that the closeness of the spacetime to the collapse threshold and charge extremality have positive correlation with the beat interval of this echo.

Automated summary

This paper explores the vibrations of quasinormal modes (QNMs) in rotating cylindrical black hole spacetime with a surrounding thin shell. The presence of the thin shell causes a piecewise metric and discontinuous potential function in the black hole spacetime beyond the horizon. Two methods, the matrix method and generalized Horowitz-Hubeny method, are proposed to solve the QNM equation with the discontinuous potential function. It is found that the thin shell can reduce the QNM frequency and alleviate the amplitude decay rate of the black hole.