# General Relativity

## General Relativity

General relativity is the theory of spacetime structure and gravitation formulated by Einstein in 1915. Present day research in general relativity focuses mainly on three major areas: (1) mathematical aspects of the classical theory of general relativity, (2) implications of the theory for astrophysics and cosmology and (3) the quantum theory of gravitation. Research in all of these areas is actively pursued at Chicago.

Although the classical theory of general relativity is a complete, well-formulated theory, the equations of the theory are sufficiently difficult to solve in general situations that we still do not know precisely what the theory predicts in a wide variety of circumstances. Thus, a great deal of effort has gone into proving general theorems about aspects such as the inevitability of gravitational collapse to singularities under a wide variety of initial conditions. In addition, because of the basic framework of the theory abandons the pre-assigned, rigid spacetime structure of special relativity, the definition of such an elementary property as the angular momentum of an isolated system becomes highly nontrivial and a number of other simple issues regarding properties of isolated systems have not been resolved. Research in these and other mathematical aspects of classical general relativity is actively pursued at Chicago, primarily by Robert Geroch.

One of the most striking consequences of general relativity is its prediction of the existence of black holes--the "regions of no escape" formed by the complete gravitational collapse of a body. It has been proven that black holes are uniquely determined by their mass, angular momentum, and electric charge, and many remarkable predictions--such as the possibility of the extraction of energy from a rotating black hole--have been made. In addition, the equations describing the propagation of small electromagnetic and gravitational disturbances near a black hole possess many remarkable properties. Research in this area has been actively pursued at Chicago.

Although general relativity is believed to be the correct classical description of gravitation, at present their exists no satisfactory quantum theory of gravitation, i.e. a theory which successfully incorporates the basic principles of both relativity and quantum theory. However, semiclassical calculation of quantum effects occurring in strong gravitational fields can be done. These quantum effects are expected to be of importance in the very early universe and near black holes. In the case of black holes, important progress was made in the mid-1970s by Hawking, who did a semiclassical calculation of the particle creation occurring in the strong gravitational field near a black hole, and obtained the remarkable result that particle are "emitted" by this process with an exactly thermal, black body spectrum. This tied together a relationship which had previously been discovered between the laws of black hole physics and those of ordinary thermodynamics and has provided a number of clues as to the nature of quantum gravity. Research on this and other issues related to quantum gravity is being actively pursued by Robert Wald.