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One of the most important methods used for finding exact solutions of the Einstein equations in four dimensions (4D) is the Petrov classification. Recent rapid development of higher dimensional gravity was motivated by string theory and large extra dimensions scenarios. In our previous joint work with A. Coley and R. Milson, we developed a generalization of the Petrov classification for higher dimensions. This classification has been already used in differential geometry, high energy physics and higher dimensional gravity but in comparison with the situation in four dimensions, possible applications remain largely unexplored. We plan to focus on these applications. We want to study certain classes of spacetimes (the Kundt class, Kerr-Schild metrics) and generalize various 4D theorems to higher dimensions. We also plan to study algebraically special classes (types N, D). Besides vacuum solutions we also plan to study solutions of the Einstein-Maxwell-Chern-Simons equations.
IM leaders:
Participating institutions:
Institute of Mathematics, AS CR
IM team members:
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Ortaggio Marcello |
Pravda Vojtěch |
