Black Hole Radiation and Evaporation

Key Insight

Despite the initial contradiction, it was discovered in 1973 that black holes do emit particles, even nonrotating ones, due to the quantum mechanical uncertainty principle. This phenomenon, known as Hawking radiation, originates not from within the black hole, but from the 'empty' space just outside the event horizon. Quantum theory posits that 'empty' space is not truly empty but filled with quantum fluctuations, which can be envisioned as pairs of virtual particles (e.g., light, gravity, or matter/antiparticle pairs) that momentarily appear and then annihilate. For such a pair, one particle has positive energy, and the other negative energy. Normally, negative energy virtual particles are short-lived, but near a black hole, the gravitational field is so intense that a virtual particle with negative energy can fall into the black hole and become a real particle. Its positive energy partner then escapes as a real particle, appearing to an observer as radiation emitted from the black hole.

This emission means black holes behave like hot bodies, with a temperature inversely proportional to their mass: the higher the mass, the lower the temperature. The flow of negative energy particles into the black hole, balancing the outgoing positive energy radiation, reduces the black hole's mass according to Einstein's E=mc². As the mass decreases, the event horizon's area shrinks. However, this decrease in the black hole's entropy (represented by its area) is more than offset by the entropy of the emitted radiation, ensuring that the second law of thermodynamics is never violated. As a black hole loses mass, its temperature and emission rate increase, accelerating its mass loss until it eventually disappears completely in a tremendous final burst of emission, equivalent to millions of H-bombs.

While large black holes (a few times the sun's mass) would have extremely low temperatures (one ten millionth of a degree above absolute zero) and evaporate over impossibly long timescales (10^66 years), primordial black holes, formed from early universe irregularities, could be much smaller, hotter, and evaporate faster. A primordial black hole with an initial mass of 1 billion tons would have a lifetime roughly equal to the universe's age. Those with slightly greater masses would still be emitting X-rays and gamma rays, making them 'white hot' and radiating about 10,000 megawatts. Although harnessing such power is currently impractical due to their tiny size and immense density, observations of the gamma ray background indicate that there cannot be more than 300 primordial black holes per cubic light-year on average, suggesting they make up at most one millionth of the universe's matter. The absence of widespread observable primordial black holes implies a very smooth and uniform early universe with high pressure.