effect

Hawking radiation

Hawking radiation is the quantum effect where black holes emit thermal radiation due to particle creation near their event horizons.
87 related articles · 1 formulas · 3 who worked here

Description

Hawking radiation arises from quantum effects at the horizon. The strong gravitational field tears apart virtual particle pairs, dooming one to fall in and letting the other escape. The escaping particle becomes real, carrying away energy. To a distant observer, the black hole emits a thermal spectrum with a temperature inversely proportional to its mass.

History

In 1971, Bekenstein proposed that the area of a black hole’s horizon is proportional to its entropy. Hawking was initially skeptical, but by 1974, applying quantum field theory in curved space (specifically, the Schwarzschild metric), he derived the existence of thermal radiation. This united thermodynamics and general relativity and gave rise to the information loss paradox, still debated today.

How it works

Near the horizon, the gravitational field gradient tidally separates virtual pairs. One particle acquires negative energy and falls in, reducing the hole’s mass; the other escapes as a real particle with positive energy. The energy spectrum is strictly Planckian with a temperature of about 6×10⁻⁸ K for a solar-mass black hole. For small primordial black holes, the temperature can be enormous, and the final stage of evaporation is an explosion. The process is universal and independent of the details of the collapse.

In practice

Shows that black holes are not eternal. Links gravity with quantum physics, a step towards a unified theory of nature.

Fun fact

A black hole with the mass of the Sun would evaporate in about 10^67 years — far longer than the age of the Universe.

Concept graph →

Formulas

$$T = \frac{\hbar c^3}{8\pi G M k_B}$$
Black hole temperature is inversely proportional to its mass.
What is in the formula
TvariableHawking temperature of the black hole — temperature kelvin
MvariableMass of the black hole — mass kilogram
\hbarconstantReduced Planck constant, fundamental quantum of action — reduced planck constant = 1.054571817e-34 joule second
cconstantSpeed of light in vacuum, universal speed limit — speed of light = 299792458 metre per second
GconstantNewtonian constant of gravitation, sets strength of gravity — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
k_BconstantBoltzmann constant, relates temperature to energy — boltzmann constant = 1.380649e-23 joule per kelvin
t\sim\frac{1}{m} · 2603.02493
t_h=\frac{ħc^3}{8πgmk_b} · 2605.13901v1
t_{bh}=\frac{m_{pl}^2}{8πm_{bh}} · 2606.03316v2
t_{bh}=\frac{1}{8πm}\sqrt{1-\frac{3(γ-3)}{2}} · 2606.26166

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