Time domain analysis of superradiant instability for the charged stringy black hole–mirror system

Abstract

It has been proved that the charged stringy black holes are stable under the perturbations of massive charged scalar fields. However, superradiant instability can be generated by adding the mirror-like boundary condition to the composed system of charged stringy black hole and scalar field. The unstable boxed quasinormal modes have been calculated by using both analytical and numerical method. In this paper, we further provide a time domain analysis by performing a long time evolution of charged scalar field configuration in the background of the charged stringy black hole with the mirror-like boundary condition imposed. We have used the ingoing Eddington-Finkelstein coordinates to derive the evolution equation, and adopted Pseudo-spectral method and the forth-order Runge-Kutta method to evolve the scalar field with the initial Gaussian wave packet. It is shown by our numerical scheme that Fourier transforming the evolution data coincides well with the unstable modes computed from frequency domain analysis. The existence of the rapid growth mode makes the charged stringy black hole a good test ground to study the nonlinear development of superradiant instability.

Evading no-hair theorems: Hairy black holes in a Minkowski box

“…Scalar fields confined inside a box were already studied in the literature: 1) at the linear level [2][3][4][5][6][14][15][16][17][18][19], 2) as a nonlinear elliptic problem (although without having flat asymptotics [7,9,10] or without discussing the exterior solution [8]), and 3) as an initial-value problem [11][12][13]. However, to the best of our knowledge, the properties of the "internal structure" of the cavity or surface layer that is necessary to confine the scalar field were never analysed.…”

“…For example, it is important to display the region of existence of each of these solutions in a mass-charge phase diagram as well as to present a microcanonical phase diagram whereby we plot the entropy of the solutions as a function of their mass and electric charge. 18 For this end, we find appropriate to work with the Brown-York quasilocal mass M and charge Q. Essentially, this is because these quasilocal quantities are independent of the parameter η that describes the energy-momentum content of the shell that confines the scalar field.…”

“…If the system has electric charge, we can also have static black hole bomb systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. All we need is a complex scalar field with charge q scattering a Reissner-Nordström black hole with chemical potential µ that is placed inside a box that reflects the scalar waves.…”

Charged black hole bombs in a Minkowski cavity

“…We can also have non-rotating superradiant black hole bomb systems, as long as the system has electric charge [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Indeed, a scalar field with charge q scattering a charged black hole with chemical potential µ can also be superradiantly amplified if the wave frequency ω satisfies the bound ω < qµ.…”

Superradiant instability of near extremal and extremal four-dimensional charged hairy black holes in anti–de Sitter spacetime

“…In our case, the change of variables that we will perform is well defined for the extremal case. So, first it is convenient to express the metric in terms of the ingoing Eddington-Finkelstein coordinate v = t + r * [50,51] ds 2 = −f (r)dv 2 + 2dvdr + a(r) 2 dσ 2 .…”