
Thermodynamic properties and quantum effects of black holes, including temperature and information.Quantum black hole thermodynamics extends classical black hole thermodynamics by incorporating quantum field theory effects. It describes black holes as thermodynamic systems with temperature (Hawking radiation), entropy (proportional to horizon area), and other state variables, while also addressing puzzles like the information paradox and the microscopic origin of entropy. This framework connects gravity, quantum mechanics, and thermodynamics, offering insights into the nature of spacetime at the quantum level.
The foundations were laid by Jacob Bekenstein in the 1970s, who proposed black hole entropy, and Stephen Hawking, who derived black hole temperature in 1974. Subsequent developments include the holographic principle and string theory calculations of microstates.
Near a black hole's horizon, quantum vacuum fluctuations become polarized, leading to the emission of thermal radiation (Hawking radiation) with a temperature inversely proportional to the black hole's mass. The entropy, given by the Bekenstein-Hawking formula, counts the microscopic quantum states of the horizon. Quantum corrections modify these relations, for example by adding logarithmic terms, and can affect how black holes evaporate or interact with surrounding fields.
These concepts guide research in quantum gravity, including attempts to resolve the information paradox, and are used to model black hole evaporation and its potential observational signatures in gravitational wave data.
A black hole with the mass of the Moon would have a temperature of about 0.001 kelvin, colder than the cosmic microwave background, so it would absorb more radiation than it emits.
| T_BKT | variable | BKT transition temperature — temperature kelvin |
| ρ_s | variable | Superfluid density at zero temperature — superfluid density kilogram per 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 |
| 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 |
| T_eff | variable | Effective temperature — temperature kelvin |
| F_lambda | variable | Spectral flux density per unit wavelength — spectral flux density watt per metre cubed |
| lambda | variable | Wavelength — wavelength metre |
| sigma | constant | Relates total blackbody flux to temperature — stefan boltzmann constant = 5.670374419e-8 watt per metre squared per kelvin to the fourth |
| ∫ | operator | Integration over all wavelengths — integral |
| ΔT/T | variable | Relative temperature fluctuation of CMB — temperature fluctuation |
| Φ | variable | Gravitational potential perturbation — gravitational potential metre squared per second squared |
| η | variable | Conformal time — conformal time second |
| ∫ | operator | Integrates over conformal time along the photon path — integral |
| dot | operator | Derivative with respect to conformal time — time derivative |





