R. Beig

Study session on static and stationary solutions to Einstein`s field equations

Scope of the session: This session complements and ties together the lecture series of Schoen, Friedrich, as well as the study session organized by Tod. The session will be longer than the other ones because of the importance of the topic, which will not be addressed directly in the morning lectures due to lack of time. There will be talks lasting from 30 to 45 minutes, and a discussion with a summary by the organizer. The following topics will be covered: Multi-black-hole configurations (G.Weinstein, University of Alabama, Birmingham); Rotating black holes and disks as explicitly solvable boundary value problems (G. Neugebauer, University of Jena); Open problems in black-hole uniqueness (P.Chrusciel, Tours); Stationary solutions and the conformal constraints: (S.Dain, AEI Institute).

Abstract of R.Beig's lecture: In this talk I reviewed rigorous results concerning asymptotically flat, time-independent solutions of the Einstein equations with sources corresponding to static or uniformly rotating bodies. The matter models discussed were perfect fluids and elastic solids. Subject to a certain differential inequality on the equation of state, it is known (Beig and Simon, Lindblom and Masood-ul-Alam) that static perfect fluids are spherically symmetric. For static elastic bodies (of arbitrary shape) there is an existence theorem for ``small'' bodies, so far only for the Newtonian theory, due to Beig and Schmidt. In the rotating case we reviewed the results of Uwe Heilig which show the existence of axisymmetric relativistic fluids for sufficiently small angular velocity and compactness. For rotating elastica nothing is known so far.

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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and R. Beig