Unusual dimensional reductions of gravity and black holes - cosmologies - wave correspondence

by Filippov, Alexander (Dubna)

Thursday 24 May 2007, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

I discuss some problems related to dimensional reductions of (super)gravity theories to two-dimensional and one-dimensional dilaton gravity models. As a first unusual example, I consider the most general cylindrical reductions of four-dimensional gravity, paying special attention to the possibility of producing non-trivial cosmological potentials from pure geometric variables. Then, a review is given of further reductions of two- dimensional theories to dimension one by applying a general procedure of separating the space and time variables (this procedure is apparently more general than the reductions using group theory). I illustrate this by the example of spherically-reduced gravity coupled to scalar matter fields. I also explain in more detail the `static-cosmological duality' and consider some unusual cosmologies and static states that can be obtained by using our procedure. The non-trivial interrelation between the static states (black holes, in particular), cosmologies, and gravitational waves is illustrated by the exact analytical solutions of a rather general integrable (1+1)-dimensional dilaton gravity. Finally, the status of this `triality' in realistic theories is outlined.