MG12 - Talk detail
 

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Abstract

Classification of the Cotton tensor in n+1 dimensions-the special 2+1 case.

The classification of Cotton tensor in n+1 dimensions is reviewed, a close to the Plebanski diagrams is given. The particular 4+1 and 2+1 dimensional spaces are studied in details, some specific spacetimes are analized.

Three-dimensional stationary cyclic symmetric Einstein-Maxwell solutions: black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2+1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possesing electromagntic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariant derivatives, all fields having constant electromagnetic invariants, the whole classes of hybrid electromagnetic solutions, and also wide classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Classes of solutions generated via sl(2R) transformations are given and properly identified.

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