Black Hole and Cosmological Particle Production Spectra

Hawking changed the way we think about black holes via his 1975 calculation that black holes with zero cosmological constant radiate quantum mechanical particles with a black body spectrum. The key feature leading to the particle production are the geometric properties of the black hole horizon, which also determine the temperature. Subsequently, Gibbons and Hawking showed that cosmological horizons also lead to a thermal spectrum. When a spacetime with positive cosmological constant, such as an Inflationary universe, contains a black hole, there are two horizons and two sources of quantum particles, but the two horizon temperatures are not equal. There are other non-standard features of the classical thermodynamics including the existence of a maximal mass (think “internal energy”) when the two horizons coincide, and a maximal total area of the horizons (think “total entropy”).

To better understand these properties, in this work-in-progress we compute the black hole and cosmological particle spectra. Since there is no asymptotically flat (think “non-interacting”) region, other criteria must be used to choose the particle states. It is found that the spectra are not thermal, except for very small black holes in which limit Hawking’s result is recovered. In the limit that the black hole approaches the maximal mass the spectra become the same and explain a saturation property of the classical spacetimes.