Charged black hole bombs in a Minkowski cavity

Abstract

Press and Teukolsky famously introduced the concept of a black hole bomb system: a scalar field scattering a Kerr black hole confined inside a mirror undergoes superradiant amplification that keeps repeating due to the reflecting boundary conditions at the mirror. A similar charged black hole bomb system exists if we have a charged scalar field propagating in a Reissner-Nordström black hole confined inside a box. We point out that scalar fields propagating in such a background are unstable not only to superradiance but also to a mechanism known as the near-horizon scalar condensation instability. The two instabilities are typically entangled but we identify regimes in the phase space where one of them is suppressed but the other is present, and vice-versa (we do this explicitly for the charged but non-rotating black hole bomb). These 'corners' in the phase space, together with a numerical study of the instabilities allow us to identify accurately the onset of the instabilities. Our results should thus be useful to make educated choices of initial data for the Cauchy problem that follows the time evolution and endpoint of the instabilities. Finally, we use a simple thermodynamic model (that makes no use of the equations of motion) to find the leading order thermodynamic properties of hairy black holes and solitons that should exist as a consequence (and that should be the endpoint) of these instabilities. In a companion publication, we explicitly solve the Einstein-Maxwell-scalar equations of motion to find the properties of these hairy solutions at higher order in perturbation theory. * Electronic address: ojcd1r13@soton.ac.uk † Electronic address: rmg1e15@soton.ac.uk

Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes

“…We discretize the field equations using a pseudospectral collocation grid on Gauss-Chebyshev-Lobbato points. The eigenvalues and respective eigenvectors are efficiently and accurately computed using a powerful numerical procedure developed in gravitational contexts in [45,46,[48][49][50][51][52][53][54][55][56][57][58][59][60] -discussed in detail in [56] and in section III.C and VI.A of the topical review [47] -which employs the Newton-Raphson root-finding algorithm. These numerical methods are very well tested in different contexts and extremely robust.…”

“…These numerical methods are very well tested in different contexts and extremely robust. In particular, they are the same that were used to compute the ultraspinning and bar-mode gravitational instabilities of rapidly spinning Myers-Perry black holes [45,46,[48][49][50][51], the near-horizon scalar condensation and superradiant instabilities of black holes [52][53][54], the gravitational superradiant instability of Kerr-AdS black holes [55,56], the electro-gravitational quasinormal modes of the Kerr-Newman black holes [57] and the modes that violate strong cosmic censorship in de Sitter backgrounds [58][59][60], to mention a few. All our results have the exponential convergence on the number of gridpoints expected for a code that uses pseudospectral collocation (see [47]).…”

A new type of charged black hole bomb

“…[10]. Working with solutions of given angular momentum, (9) reduces to a partial differential equation in 1 + 1-dimensions:…”

“…These charged black hole bombs have been somewhat less investigated than their rotating analogues but there is still a fair amount of studies, mostly numerical, available in the literature, for instance Ref. [4,8,9,14,17,18].…”

Phase structures and transitions of Born–Infeld black holes in a grand canonical ensemble

“…In [24][25][26][27], boson stars and hairy black holes in a cavity were considered, and it showed that the phase structure of the gravity system in a cavity is strikingly similar to that of holographic superconductors in the AdS gravity. The stabilities of solitons, stars and black holes in a cavity were also studied in [28][29][30][31][32][33][34][35], which showed that the nonlinear dynamical evolution of a charged black hole in a cavity could end in a quasi-local hairy black hole. The thermodynamic behavior of de Sitter black holes in a cavity has been discussed in the extended phase space [36].…”