Scalar clouds in charged stringy black hole-mirror system

Abstract

It was reported that massive scalar fields can form bound states around Kerr black holes (Herdeiro and Radu, Phys. Rev. Lett. 112:221101, 2014). These bound states are called scalar clouds; they have a real frequency ω = m H , where m is the azimuthal index and H is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition ω = q H for a charged scalar field, where q is the charge of the scalar field, and H is the horizon's electrostatic potential. We show that, for the specific set of black hole and scalar field parameters, the clouds are only possible for specific mirror locations r m . It is shown that analytical results of the mirror location r m for the clouds perfectly coincide with numerical results in the q Q 1 regime. We also show that the scalar clouds are also possible when the mirror locations are close to the horizon. Finally, we provide an analytical calculation of the specific mirror locations r m for the scalar clouds in the q Q 1 regime.

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.…”

“…At least for small charges where our perturbative analysis is valid, hairy black holes can be the dominant thermal phase only in the microcanonical ensemble so we restrict our discussion to this ensemble. 19 Essentially, these different solutions differ from each other in the interior region and the energy-momentum content of this region is best captured by the quasilocal thermodynamics. Further recall that these quasilocal quantities obey the quasilocal first law of thermodynamics (2.31) and (2.32), which we used to check our final results.…”

“…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.…”

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

“…For a small BH, the left term in Eqs. (28) and (29) vanish at the leading order, then we have to require the right term in both equations to vanish as well. These conditions give the normal modes for pure AdS,…”

Stationary charged scalar clouds around black holes in string theory

“…A static spherical symmetric charged black hole in the low energy limit of heterotic string field theory in four dimensions was first found by Gibbons and Maeda in [13] and independently obtained by Garfinkle, Horowitz, and Strominger in [14] three years later. The metric that describes this GMGHS spacetime is [21]…”