phenomenon

black hole scalar clouds

Long-lived scalar field configurations surrounding rotating black holes.
13 related articles · 6 formulas

Description

Black hole scalar clouds are long-lived configurations of a scalar field that can exist in the vicinity of a rotating black hole. Unlike ordinary matter that falls into a black hole, these clouds are held in a delicate balance: the black hole's gravity pulls the field inward, while the rotation of the black hole provides a mechanism to extract energy and angular momentum, preventing the field from collapsing. This creates a self-sustaining structure that can persist for very long times, effectively acting as an 'atmosphere' or 'cloud' around the black hole.

History

The concept of scalar clouds around black holes emerged from studies of superradiance in the 1970s, with key theoretical groundwork laid by Press and Teukolsky, and later developed in the context of ultralight bosonic fields. The specific term 'scalar clouds' and their detailed properties were explored extensively in the 2010s.

How it works

The mechanism relies on a phenomenon called superradiance. When a wave or field perturbation scatters off a rotating black hole, it can be amplified, extracting rotational energy from the black hole in the process. If the scalar field has a mass, it can be trapped in the vicinity of the black hole by its gravitational pull, bouncing back and forth. With each bounce, the field is amplified by superradiance, leading to the growth of a cloud. The cloud's growth is eventually limited by nonlinear effects or by the gradual spin-down of the black hole, after which it reaches a stable, long-lived configuration.

In practice

These clouds are studied as potential signatures of ultralight bosonic particles (like axions) and as sources of continuous gravitational waves, which could be detected by observatories like LIGO and LISA.

Fun fact

The existence of a scalar cloud can slow down a black hole's rotation over time, effectively acting as a cosmic brake.

Concept graph →

Formulas

$$r_{\pm} = \frac{GM}{c^2} \left(1 \pm \sqrt{1 - \frac{k_e Q^2}{G M^2}}\right)$$
Locations of event horizons in charged black holes.
What is in the formula
r_±variableInner and outer event horizon radii — horizon radius metre
QvariableElectric charge of the black hole — electric charge coulomb
MvariableMass of the black hole — mass kilogram
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared
r_{\pm}=\frac{gm}{c^2}(1\pm\sqrt{1-\xi}) · 2605.10587v1
$$M_{\text{PBH}} \propto k_p^{-2}$$
Primordial black hole mass scales with perturbation scale.
What is in the formula
M_PBHvariablePrimordial black hole mass — mass kilogram
k_pvariablePerturbation wavenumber — wavenumber per metre
∝operatorProportional to — proportionality
m_{\rmpbh}\approx30m_\odot(\frac{g_*}{10.75})^{-1/6}(\frac{k_p}{2.9*10^5{\rmmpc}^{-1}})^{-2} · 2607.01818
$$\Box \varphi = -4\pi \rho$$
The wave equation for a scalar field with a source term.
What is in the formula
\varphivariablescalar field — scalar field
\rhovariablesource density — source density per cubic metre
\BoxoperatorLorentz-invariant second-order differential operator — d alembertian operator
\box\varphi^{(1)}=-4πdμ\int\frac{δ^{(4)}(x-y_p(τ))}{\sqrt{-g}}dτ · 2607.09310
$$\Delta(r) = r^2 - 2Mr + a^2 + Q^2$$
Horizon function for charged rotating black holes with charge Q.
What is in the formula
rvariableradial coordinate — radial coordinate metre
Mvariableblack hole mass — mass kilogram
avariablespecific angular momentum (spin parameter) — angular momentum per unit mass metre
Qvariableelectric charge — electric charge coulomb
δ_{{ed}}(r)=r^2-2mr+a^2+q · 2607.13992
$$P(k) \propto k^{n} \sin[\rho \ln(k) + \phi]$$
Power spectrum oscillations from massive fields imprint logarithmic oscillations.
What is in the formula
P(k)variablepower spectrum as function of wavenumber — power spectrum cubic metre
kvariablewavenumber — wavenumber reciprocal metre
nvariablespectral index — spectral index
ρvariableoscillation frequency parameter — oscillation frequency parameter
φvariablephase offset — phase radian
lnoperatortakes the natural logarithm of its argument — natural logarithm
sinoperatorcomputes the sine of the argument — sine function
s(k_s,k_s,k_l)\propto(\frac{k_l}{k_s})^{1/2}c(λ,ρ)\sin[ρ\ln(\frac{k_s}{k_l})+φ] · 2607.14529
$$r_{\text{ISCO}} = r_g \left[3 + Z_2 \mp \sqrt{(3-Z_1)(3+Z_1+2Z_2)}\right]$$
Radius of the innermost stable circular orbit around a Kerr black hole.
What is in the formula
r_{\text{ISCO}}variableradius of the innermost stable circular orbit — radius metre
r_gvariablegravitational radius (GM/c^2) — radius metre
Z_1variableauxiliary function of spin parameter a
Z_2variableauxiliary function of spin parameter a
\mpoperatorindicates two possible solutions depending on orbital direction — minus plus sign
\sqrt{}operatortakes the square root of the argument — square root
r_{{isco}}=r_g[3+z_2\mp\sqrt{(3-z_1)(3+z_1+2z_2)}],\quadz_1=1+(1-a^2)^{1/3}[(1+a)^{1/3}+(1-a)^{1/3}],\quadz_2=\sqrt{3a^2+z_1^2} · 2607.22418v1

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