phenomenon

black hole resonance

A black hole resonates with surrounding matter or fields, amplifying waves or creating scalar clouds.
15 related articles · 6 formulas

Description

Black hole resonance refers to the phenomenon where a rotating black hole interacts with surrounding matter or fields, amplifying certain waves or creating stable 'clouds' of particles. The most famous example is superradiance: when waves of the correct frequency hit a rotating black hole, they can extract rotational energy, growing in amplitude. If the waves are massive (like a scalar field), they can become trapped in the black hole's vicinity, forming a gravitational atom-like cloud that grows over time. This resonance is a key mechanism for probing black hole properties and for explaining certain astrophysical signals.

History

The concept of superradiance was predicted by Roger Penrose in 1969 and generalized to waves by Yakov Zel'dovich in 1971. The idea of scalar clouds around black holes was developed in the 1970s and revived in the 2010s as a potential dark matter probe.

How it works

The mechanism relies on the ergosphere of a rotating black hole, where spacetime itself is dragged along the rotation. A wave entering this region can be scattered with increased energy if its frequency is lower than the black hole's angular velocity. For massive fields, the wave can be bound in a potential well created by the black hole's gravity and the field's mass, leading to repeated amplification — a 'black hole bomb' if unchecked. The growth rate depends on the field mass and the black hole's spin, and the resulting cloud emits gravitational waves, which could be detected by observatories like LIGO.

In practice

Black hole resonance is used to test the no-hair theorem, to constrain the mass of ultralight bosons (dark matter candidates), and to explain gaps in the observed mass spectrum of black holes. It also provides a mechanism for generating gravitational wave signals from otherwise quiet black holes.

Fun fact

The 'black hole bomb' — where a mirror around the black hole causes superradiant waves to grow exponentially — was proposed in 1972 and later shown to be a natural consequence of massive fields, potentially limiting the spin of astrophysical black holes.

Concept graph →

Formulas

$$M_{\rm BH} \propto L^\alpha \, {\rm FWHM}^\beta$$
Black hole mass scales with luminosity and line width.
What is in the formula
M_BHvariableBlack hole mass — mass kilogram
LvariableContinuum luminosity (e.g., at 5100 Å) — luminosity watt
FWHMvariableFull width at half maximum of emission line — line width metre per second
αvariablePower-law index for luminosity — power law index
βvariablePower-law index for line width — power law index
m_{\rmbh}=a(\frac{l_{5100}}{10^{44}{\rmэрг/с}})^b(\frac{{\rmfwhm}_{\rmhα}}{v_{\rmnorm}})^c · 2606.06226v1
m_{{bh}}\proptol_{{h}α}^{0.55}*{fwhm}_{{h}α}^{2.06} · 2607.01330v1
$$f_{\text{high}} \propto f_{\text{low}}^2$$
High frequency scales with square of low frequency.
What is in the formula
f_{\text{high}}variableHigh frequency — frequency hertz
f_{\text{low}}variableLow frequency — frequency hertz
f_{\rmisco}\approx3.4*10^{20}{\rmhz}(\frac{f_{\rmsigw}}{\rmhz})^2 · 2607.01818
$$\omega = m \Omega_{\rm H}$$
Scalar cloud frequency equals azimuthal quantum number times horizon angular velocity.
What is in the formula
ωvariableFrequency of the scalar field mode — angular frequency radian per second
mvariableAzimuthal quantum number of the mode — azimuthal quantum number
Ω_HvariableAngular velocity of the black hole horizon — angular velocity radian per second
ω=mω_{\rmh} · 2607.28044v1
$$A = 8\pi M \left(M + \sqrt{M^2 - a^2}\right)$$
The area of a Kerr black hole depends on mass and spin.
What is in the formula
AvariableArea of the event horizon — area square metre
MvariableMass of the black hole — mass kilogram
avariableSpecific angular momentum (angular momentum per unit mass) — specific angular momentum metre
πconstantRatio of a circle's circumference to its diameter — pi = 3.14159
a=8πm^2(1+\sqrt{1-a^2}) · 2606.06592v1
$$f_n = n f_0$$
Harmonic frequencies are integer multiples of fundamental frequency.
What is in the formula
f_nvariablefrequency of the nth harmonic — frequency hertz
nvariableharmonic number (positive integer)
f_0variablefundamental frequency — frequency hertz
f_n=nf_0 · 2607.12315
$$M_{\text{PBH}} \propto k_p^{-2}$$
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

Related articles · 15

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