Black hole thermodynamics describes the thermal properties and entropy of black holes through analogies with classical thermodynamics.Black hole thermodynamics is a framework that treats black holes as thermodynamic systems with temperature, entropy, and energy, despite their classical description as objects that only absorb. The key results are that a black hole's entropy is proportional to its event horizon area (Bekenstein-Hawking entropy) and its temperature is inversely proportional to its mass (Hawking temperature). This theory bridges general relativity, quantum mechanics, and thermodynamics, revealing deep connections between gravity and statistical mechanics.
The framework was developed in the early 1970s by Jacob Bekenstein, who proposed entropy proportional to area, and Stephen Hawking, who derived black hole radiation in 1974, completing the thermodynamic picture.
The analogy works because black holes obey laws mathematically identical to the laws of thermodynamics: the zeroth law defines a constant surface gravity (temperature), the first law relates mass change to area change (energy and entropy), and the second law states that horizon area never decreases. Hawking's quantum calculation showed that black holes emit thermal radiation, giving the temperature a real physical meaning: smaller black holes are hotter and radiate more intensely.
It guides theoretical research in quantum gravity, holography (AdS/CFT correspondence), and cosmological models, and helps interpret observations of black hole mergers and shadows.
A black hole with the mass of the Moon would have a temperature of about 0.1 kelvin, while a solar-mass black hole is far colder than the cosmic microwave background at 60 nanokelvin.
| T | variable | Hawking temperature of the black hole — temperature kelvin |
| M | variable | Mass of the black hole — mass kilogram |
| \hbar | constant | Reduced Planck constant, fundamental quantum of action — reduced planck constant = 1.054571817e-34 joule second |
| c | constant | Speed of light in vacuum, universal speed limit — speed of light = 299792458 metre per second |
| G | constant | Newtonian constant of gravitation, sets strength of gravity — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| k_B | constant | Boltzmann constant, relates temperature to energy — boltzmann constant = 1.380649e-23 joule per kelvin |
| S | variable | Entropy of the black hole — entropy joule per kelvin |
| A | variable | Area of the event horizon — area square metre |
| k | constant | Boltzmann constant — boltzmann constant = 1.380649e-23 joule per kelvin |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| ħ | constant | Reduced Planck constant — reduced planck constant = 1.054571817e-34 joule second |
| S | variable | Black hole entropy — entropy joule per kelvin |
| A | variable | Black hole horizon area — area square metre |
| T_bb | variable | Blackbody temperature — temperature kelvin |
| M | variable | Mass of the accreting object — mass kilogram |
| a | variable | Positive exponent for mass scaling |
| dot_m | variable | Mass accretion rate — mass flow rate kilogram per second |
| b | variable | Positive exponent for accretion rate scaling |
| ∝ | operator | Proportional to — proportionality |
| T_H | variable | Hawking temperature of the black hole — temperature kelvin |
| κ | variable | surface gravity of the black hole — surface gravity metre per second squared |
| ħ | constant | fundamental constant equal to h/(2π), relating angular frequency to energy — reduced planck constant = 1.054571817e-34 joule second |
| k_B | constant | fundamental constant relating temperature to energy — boltzmann constant = 1.380649e-23 joule per kelvin |











