Long-lived scalar field configurations surrounding rotating black holes.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.
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.
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.
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.
The existence of a scalar cloud can slow down a black hole's rotation over time, effectively acting as a cosmic brake.
| r_± | variable | Inner and outer event horizon radii — horizon radius metre |
| Q | variable | Electric charge of the black hole — electric charge coulomb |
| M | variable | Mass of the black hole — mass kilogram |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| k_e | constant | Electrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared |
| M_PBH | variable | Primordial black hole mass — mass kilogram |
| k_p | variable | Perturbation wavenumber — wavenumber per metre |
| ∝ | operator | Proportional to — proportionality |
| \varphi | variable | scalar field — scalar field |
| \rho | variable | source density — source density per cubic metre |
| \Box | operator | Lorentz-invariant second-order differential operator — d alembertian operator |
| r | variable | radial coordinate — radial coordinate metre |
| M | variable | black hole mass — mass kilogram |
| a | variable | specific angular momentum (spin parameter) — angular momentum per unit mass metre |
| Q | variable | electric charge — electric charge coulomb |
| P(k) | variable | power spectrum as function of wavenumber — power spectrum cubic metre |
| k | variable | wavenumber — wavenumber reciprocal metre |
| n | variable | spectral index — spectral index |
| ρ | variable | oscillation frequency parameter — oscillation frequency parameter |
| φ | variable | phase offset — phase radian |
| ln | operator | takes the natural logarithm of its argument — natural logarithm |
| sin | operator | computes the sine of the argument — sine function |
| r_{\text{ISCO}} | variable | radius of the innermost stable circular orbit — radius metre |
| r_g | variable | gravitational radius (GM/c^2) — radius metre |
| Z_1 | variable | auxiliary function of spin parameter a |
| Z_2 | variable | auxiliary function of spin parameter a |
| \mp | operator | indicates two possible solutions depending on orbital direction — minus plus sign |
| \sqrt{} | operator | takes the square root of the argument — square root |






