The modern theory of gravity is Einstein's general relativity. In most situations it gives results almost identical to Newton's theory of gravity and the latter is sufficient for practical applications. One place where general relativity becomes essential in order to describe physical phenomena is in explaining astronomical observations. This is particularly true in the study of the early history of our universe and of the fate of stars which have exhausted their supply of energy. Among the physical situations which could not otherwise be understood are the initial singularity of our universe (big bang) and the black holes which arise from the gravitational collapse of matter.
General relativity is a theory which requires the application of advanced mathematical techniques. The central role is played by the Einstein equations. Although these equations have been known for the best part of a century we still only have a limited overview of what their solutions look like in general. One of the main themes of my research is the attempt to obtain more precise and extensive information about solutions of these equations. A typical approach is to carry out detailed studies of particular classes of solutions which have the potential to lead to insights of more general applicability.
Since solutions of the Einstein equations are so hard to work with, physicists often turn to approximate versions of the equations in order to obtain concrete predictions. This may be done by neglecting certain parts of the full equations which are believed to be of little importance. A complementary procedure is to use computers to solve the equations numerically, a method which also involves approximations, due to the limited amount of data computers can handle. There remains the task of assessing the reliability of these approximate schemes. To what extent do their results reflect the properties of solutions of the exact equations? This kind of assessment is also a theme of my work.
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