Hawking Radiation
In classical general relativity, a black hole is an object with a gravitational field so intense that its escape velocity exceeds the speed of light. Nothing can escape from within the event horizon. However, in 1974, Stephen Hawking demonstrated that when quantum field theory is formulated in the curved spacetime background of a black hole, the black hole must emit thermal radiation.
Quantum Field Theory in Curved Spacetime
In quantum field theory, the vacuum is not a simple, empty void. It is subject to quantum fluctuations, often visualized as the continuous creation and annihilation of virtual particle-antiparticle pairs. In flat spacetime, these pairs annihilate almost instantly, conserving energy globally.
However, near the event horizon of a black hole, the strong gravitational tidal forces can separate these virtual pairs. If one particle falls into the black hole while the other escapes to infinity, the escaping particle becomes a real particle. To an external observer, the black hole appears to be emitting radiation.
Black Hole Thermodynamics
The emission of Hawking radiation implies that black holes possess a temperature, known as the Hawking temperature, which is inversely proportional to the black hole's mass:
Where $\hbar$ is the reduced Planck constant, $c$ is the speed of light, $G$ is the gravitational constant, $M$ is the mass of the black hole, and $k_B$ is the Boltzmann constant.
Because the emitted radiation carries energy away, the black hole must lose mass to conserve energy ($E = mc^2$). As the mass decreases, the temperature increases, leading to an accelerating rate of evaporation. Eventually, the black hole will completely evaporate in a final flash of high-energy radiation.
The Information Paradox
The discovery of Hawking radiation led to one of the most significant unresolved problems in theoretical physics: the black hole information paradox. According to quantum mechanics, physical information cannot be permanently destroyed. However, Hawking radiation is perfectly thermal, meaning it depends only on the black hole's mass, charge, and angular momentum. It contains no information about the matter that originally formed the black hole. If the black hole completely evaporates into featureless thermal radiation, what happens to the original information? Resolving this paradox requires a complete theory of quantum gravity.