Stationary scalar configurations around extremal charged black holes

Abstract

We consider the minimally coupled Klein-Gordon equation for a charged, massive scalar field in the non-extremal Reissner-Nordström background. Performing a frequency domain analysis, using a continued fraction method, we compute the frequencies ωfor quasi-bound states. We observe that, as the extremal limit for both the background and the field is approached, the real part of the quasi-bound states frequencies $\mathcal{R}(\omega )$ tends to the mass of the field and the imaginary part $\mathcal{I}(\omega )$ tends to zero, for any angular momentum quantum number $\ell$. The limiting frequencies in this double extremal limit are shown to correspond to a distribution of extremal scalar particles, at stationary positions, in no-force equilibrium configurations with the background. Thus, generically, these stationary scalar configurations are regular at the event horizon. If, on the other hand, the distribution contains scalar particles at the horizon, the configuration becomes irregular therein, in agreement with no hair theorems for the corresponding Einstein-Maxwell-scalar field system.

5 pages, 4 figures

Cited by in corpus (67)

• Kerr-Newman scalar clouds
• Kerr-Newman black holes with stationary charged scalar clouds
• Kerr black holes with self-interacting scalar hair: hairier but not heavier
• Black holes and fundamental fields in Numerical Relativity: initial data construction and evolution of bound states
• Bardeen Regular Black Hole With an Electric Source
• Time evolution of superradiant instabilities for charged black holes in a cavity
• Non-linear Q-clouds around Kerr black holes
• Myers-Perry black holes with scalar hair and a mass gap
• Stability of highly-charged Reissner-Nordström black holes to charged scalar perturbations
• Exploring New Physics Frontiers Through Numerical Relativity
• Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity
• The large-mass limit of cloudy black holes
• Extremal Kerr-Newman black holes with extremely short charged scalar hair
• The superradiant instability regime of the spinning Kerr black hole
• Rotating black holes can have short bristles
• Spherical electro-vacuum black holes with resonant, scalar $Q$-hair
• Quasinormal modes of charged fields around a Reissner-Nordström black hole
• Marginal scalar and Proca clouds around Reissner-Nordström black holes
• Maxwell perturbations on Kerr-anti-de Sitter: quasinormal modes, superradiant instabilities and vector clouds
• Scalar field configurations supported by charged compact reflecting stars in a curved spacetime
• No-scalar-hair theorem for spherically symmetric reflecting stars
• Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell
• Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime
• On the instability for massive scalar fields in Kerr-Newman spacetime
• Acoustic clouds: standing sound waves around a black hole analogue
• Stationary Charged Scalar Clouds around Black Holes in String Theory
• The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
• Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation
• Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell
• Scalar clouds around Kerr-Sen black holes
• Time domain analysis of superradiant instability for the charged stringy black hole-mirror system
• Stationary scalar clouds around a BTZ black hole
• Scalar clouds in charged stringy black hole-mirror system
• Static scalar field condensation in regular asymptotically AdS reflecting star backgrounds
• Stationary bound-state scalar configurations supported by rapidly-spinning exotic compact objects
• The longlived charged massive scalar field in the higher-dimensional Reissner--Nordström spacetime
• Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes
• Late-time tails, entropy aspects, and stability of black holes with anisotropic fluids
• Instability and no-hair paradigm in d-dimensional charged-AdS black holes
• Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime
• Scalar condensation behaviors around regular Neuman reflecting stars
• Superradiance of charged black holes in Einstein-Gauss-Bonnet Gravity
• Dirac dynamical resonance states around Schwarzschild black holes
• Hair formation in the background of noncommutative reflecting stars
• Time evolutions of scalar field perturbations in $D$-dimensional Reissner-Nordström Anti-de Sitter black holes
• On the (non) existence of superregular boson clouds around extremal Kerr black holes and its connection with number theory
• Superradiantly stable non-extremal Reissner-Nordstrom black holes
• The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror
• Charged Dirac perturbations on Reissner-Nordström-Anti-de Sitter spacetimes: quasinormal modes with Robin boundary conditions
• Analytical Study of a Kerr-Sen Black Hole and a Charged Massive Scalar Field
• No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions
• Large regular reflecting stars have no scalar field hair
• Stationary scalar hairy configurations supported by Neumann compact stars
• Quasibound states of the Dirac field in Schwarzschild and Reissner-Nordström black hole backgrounds
• No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars
• No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars
• No-go theorem for static boson stars with negative cosmological constants
• No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity
• $D=5$ static, charged black holes, strings and rings with resonant, scalar $Q$-hair
• How short can stationary charged scalar hair be?
• A no-go theorem for scalar fields with couplings from Ginzburg-Landau models
• No scalar condensations outside reflecting stars with coupling terms from Ginzburg-Landau models
• Regular scalar charged clouds around a Reissner-Nordstrom black hole and no-hair theorems
• Superradiance and instabilities in black holes surrounded by anisotropic fluids
• Analytical investigations on non-minimally coupled scalar fields outside neutral reflecting shells