The large-mass limit of cloudy black holes

Abstract

The interplay between black holes and fundamental fields has attracted much attention over the years from both physicists and mathematicians. In this paper we study {\it analytically} a physical system which is composed of massive scalar fields linearly coupled to a rapidly-rotating Kerr black hole. Using simple arguments, we first show that the coupled black-hole-scalar-field system may possess stationary bound-state resonances (stationary scalar `clouds') in the bounded regime $1<\mu /m{\Omega }_{\text{H}}<\sqrt{2}$, where $\mu$ and $m$ are respectively the mass and azimuthal harmonic index of the field, and ${\Omega }_{\text{H}}$ is the angular velocity of the black-hole horizon. We then show explicitly that these two bounds on the dimensionless ratio $\mu /m{\Omega }_{\text{H}}$ can be saturated in the asymptotic $m\to \infty$ limit. In particular, we derive a remarkably simple analytical formula for the resonance mass spectrum of the stationary bound-state scalar clouds in the regime $M\mu \gg 1$ of large field masses: ${\mu }_n=\sqrt{2}m{\Omega }_{\text{H}}[1-\frac{\pi (\mathcal{R}+n)}{m|\ln \tau |}]$, where $\tau$ is the dimensionless temperature of the rapidly-rotating (near-extremal) black hole, $\mathcal{R}<1$ is a constant, and $n=0,1,2,...$ is the resonance parameter. In addition, it is shown that, contrary to the flat-space intuition, the effective lengths of the scalar field configurations in the curved black-hole spacetime approach a {\it finite} asymptotic value in the large mass $M\mu \gg 1$ limit. In particular, we prove that in the large mass limit, the characteristic length scale of the scalar clouds scales linearly with the black-hole temperature.

arXiv comment21 pages. Invited contribution to the Focus Issue on "Black holes and fundamental fields", Classical and Quantum Gravity

References in corpus (39)

• Kerr black holes with scalar hair
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• The black hole bomb and superradiant instabilities
• Superradiant instabilities in astrophysical systems
• Stationary Scalar Clouds Around Rotating Black Holes
• Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
• No hair for spherical black holes: charged and nonminimally coupled scalar field with self--interaction
• Instability of Massive Scalar Fields in Kerr-Newman Spacetime
• Superradiant instabilities of rotating black holes in the time domain
• Kerr-Newman scalar clouds
• Rapid growth of superradiant instabilities for charged black holes in a cavity
• Weak Cosmic Censorship: As Strong as Ever
• Stationary resonances of rapidly-rotating Kerr black holes
• Kerr-Newman black holes with stationary charged scalar clouds
• On the instability regime of the rotating Kerr spacetime to massive scalar perturbations
• Black holes and fundamental fields in Numerical Relativity: initial data construction and evolution of bound states
• Classes of Exact Solutions to the Teukolsky Master Equation
• Time evolution of superradiant instabilities for charged black holes in a cavity
• Holographic Derivation of Kerr-Newman Scattering Amplitudes for General Charge and Spin
• Hairy Black Holes and Null Circular Geodesics
• A new spin on black hole hair
• Non-linear Q-clouds around Kerr black holes
• Myers-Perry black holes with scalar hair and a mass gap
• Stationary scalar configurations around extremal charged black holes
• Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime
• Rotating black holes can have short bristles
• Teukolsky-Starobinsky Identities - a Novel Derivation and Generalizations
• New instability for rotating black branes and strings
• Black hole bombs and explosions: from astrophysics to particle physics
• Instability of rotating black hole in a limited form of $f(R)$ gravity
• Marginal scalar and Proca clouds around Reissner-Nordström black holes
• Onset of superradiant instabilities in the composed Kerr-black-hole-mirror bomb
• Superradiant instability of the charged scalar field in stringy black hole mirror system
• On the stability of the massive scalar field in Kerr space-time
• Stability of charged black holes in string theory under charged massive scalar perturbations
• Asymptotic spectrum of the oblate spin-weighted spheroidal harmonics: a WKB analysis
• Black-hole perturbation theory: The asymptotic spectrum of the prolate spin-weighted spheroidal harmonics
• Analytical study of superradiant instability for five-dimensional Kerr-Gödel black hole
• Superradiance by mini black holes with mirror

Cited by in corpus (54)

• Kerr black holes with Proca hair
• Kerr black holes with self-interacting scalar hair: hairier but not heavier
• Iron K$\alpha$ line of Kerr black holes with scalar hair
• Kerr black holes with synchronised hair: an analytic model and dynamical formation
• Extremal Kerr-Newman black holes with extremely short charged scalar hair
• The superradiant instability regime of the spinning Kerr black hole
• Inside black holes with synchronized hair
• Kerr-Newman black holes with scalar hair
• Excited Kerr black holes with scalar hair
• Scalar clouds and the superradiant instability regime of Kerr-Newman black hole
• 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
• Black holes with synchronised Proca hair: linear clouds and fundamental non-linear solutions
• Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime
• On the instability for massive scalar fields in Kerr-Newman spacetime
• The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
• Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index
• Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field
• Charged reflecting stars supporting charged massive scalar field configurations
• 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
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• Stationary scalar clouds around a BTZ black hole
• Onset of superradiant instabilities in rotating spacetimes of exotic compact objects
• Static scalar field condensation in regular asymptotically AdS reflecting star backgrounds
• Acoustic black-hole bombs and scalar clouds in a photon-fluid model
• No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields
• Stationary bound-state scalar configurations supported by rapidly-spinning exotic compact objects
• Slowly decaying resonances of massive scalar fields around Schwarzschild-de Sitter black holes
• Charged black holes in non-linear Q-clouds with O(3) symmetry
• Rotating tensor-multiscalar black holes with two scalars
• Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime
• Hair formation in the background of noncommutative reflecting stars
• No hair for spherically symmetric neutral reflecting stars: nonminimally coupled massive scalar fields
• Ultra-spinning exotic compact objects supporting static massless scalar field configurations
• The Reissner-Nordström black hole with the fastest relaxation rate
• Black holes, stationary clouds and magnetic fields
• No-go theorem for static boson stars
• The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror
• No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions
• Synchronized stationary clouds in a static fluid
• Large regular reflecting stars have no scalar field hair
• No-short scalar hair theorem for spinning acoustic black holes in a photon-fluid model
• Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars
• Stationary scalar clouds supported by rapidly-rotating acoustic black holes in a photon-fluid model
• Stationary scalar hairy configurations supported by Neumann compact stars
• No-go theorem for static boson stars with negative cosmological constants
• No-go theorem for spatially regular boson stars made of static nonminimally coupled massive scalar fields
• Reissner-Nordström black holes with non-Abelian hair
• How short can stationary charged scalar hair be?
• On instabilities of stationary scalar field configurations supported by reflecting compact stars