Beyer 200805

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In the field of Einstein's general relativity, promising successes have been achieved. This is the case both for the understanding of the nature of the theory, and for qualitative and quantitative aspects, since the formulation of Einstein's field equations (EFE) as a Cauchy problem about 50 years ago. Nevertheless, there are several serious outstanding questions at the very heart of the theory. One of those issues is the following. In order to simplify the discussion, let us neglect all matter fields and restrict to 'pure gravity'. Suppose that -- in a well defined sense -- one prescribes the 'state' of spacetime at some initial time, the initial data. Due to results by Choquet-Bruhet and others, there always exists a unique spacetime corresponding to these data in a local time neighborhood of the initial time which is a solution of EFE. Now, let us extend this spacetime in time as a solution of EFE such that the paths of all observers starting from the initial time are included completely. Is this extended spacetime always unique? The hope was that the answer is yes because otherwise Einstein's theory would have only limited predictive power. However, certain counter examples were found, one of them is the family of Taub-NUT solutions. Nevertheless, there are reasons to believe that all known examples of this kind are 'non-generic' in a certain sense, and the conjecture, called strong cosmic censorship conjecture, is that for 'generic' solutions, Einstein's theory retrieves its 'global' predictive power. Analytical and numerical attempts to shed light on such aspects have been undertaken since many years. Although one was able to prove the strong cosmic censorship conjecture only in certain symmetry classes so far, these studies have revealed interesting new insides.

After having introduced the necessary background and given some comments on the current state of knowledge on strong cosmic censorship, I will discuss some of my studies of non-linear perturbations of Taub-NUT spacetimes with my own numerical code based on spectral methods.

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