Black hole accretion is the process by which matter falls into a black hole, often producing radiation and outflows.Black hole accretion is the process by which matter spirals into a black hole, forming a hot, glowing disk that can outshine entire galaxies. As gas and dust fall inward, they gain enormous kinetic energy, which is converted into heat and radiation through friction and magnetic stresses. This process is the primary way black holes are detected, as the accretion disk emits X-rays, visible light, and radio waves long before the matter crosses the event horizon.
The concept was developed in the 1970s, with key contributions from Nikolai Shakura and Rashid Sunyaev, who formulated the standard thin-disk model in 1973.
Matter with angular momentum doesn't fall straight in; it forms a rotating disk. Viscous forces and magnetic instabilities within the disk transport angular momentum outward, allowing material to slowly drift inward. As it approaches the black hole, gravitational potential energy is released, heating the disk to millions of degrees. Some of this energy powers relativistic jets—narrow beams of plasma ejected along the black hole's spin axis—while the rest emerges as radiation from the disk's surface.
Accretion disk models are used to estimate black hole masses in active galactic nuclei and X-ray binaries, and to interpret observations from telescopes like the Event Horizon Telescope.
The luminosity of an accretion disk can reach a limit called the Eddington limit, where the outward pressure of radiation balances the inward pull of gravity, causing the disk to blow away material in powerful winds.
| L_{\rm acc} | variable | accretion luminosity — luminosity watt |
| M | variable | mass of the accreting object — mass kilogram |
| \dot{M} | variable | mass accretion rate — mass flow rate kilogram per second |
| R | variable | radius at which accretion energy is released — radius metre |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| P | variable | accretion power — power watt |
| η | variable | efficiency of mass-to-energy conversion |
| Ṁ | variable | mass accretion rate — mass flow rate kilogram per second |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| \dot{M} | variable | mass accretion rate — mass accretion rate kilogram per second |
| M | variable | mass of the gravitating body — mass kilogram |
| \rho_\infty | variable | ambient gas density at infinity — mass density kilogram per cubic metre |
| c_s | variable | sound speed in the gas — speed metre per second |
| v_{\text{rel}} | variable | relative velocity of the body through the gas — velocity metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \lambda | constant | dimensionless accretion efficiency factor of order unity — accretion efficiency = 1 |
| M | variable | Black hole mass at time t — mass kilogram |
| M_0 | variable | Initial black hole mass — mass kilogram |
| t | variable | Time since start of evaporation — time second |
| τ | variable | Total evaporation timescale — time second |
| 1 - t/τ | operator | Computes the fraction of remaining lifetime — linear combination |
| ( )^{1/3} | operator | Takes the cube root of the remaining fraction — cube root |
| r_H | variable | Accretion horizon radius — radius metre |
| \dot{M} | variable | Mass accretion rate — mass flow rate kilogram per second |
| \rho | variable | Mass density of accreting material — mass density kilogram per cubic metre |
| c_s | variable | Sound speed in accreting material — speed metre per second |
| S | variable | Black hole entropy — entropy joule per kelvin |
| A | variable | Black hole horizon area — area square metre |












