/ Gravitation and Cosmology hep-th/0612258


Dimensional reduction of gravity and relation between static states, cosmologies and waves


de Alfaro, Vittorio (INFN, Turin) ; Filippov, A.T. (Dubna, JINR)

Published in: Theor.Math.Phys.
Year: 2007
Vol.: 153
Page No: 1709-1731
Pages: 25

Abstract: We introduce generalized dimensional reductions of an integrable 1+1-dimensional dilaton gravity coupled to matter down to one-dimensional static states (black holes in particular), cosmological models and waves. An unusual feature of these reductions is the fact that the wave solutions depend on two variables - space and time. They are obtained here both by reducing the moduli space (available due to complete integrability) and by a generalized separation of variables (applicable also to non integrable models and to higher dimensional theories). Among these new wave-like solutions we have found a class of solutions for which the matter fields are finite everywhere in space-time, including infinity. These considerations clearly demonstrate that a deep connection exists between static states, cosmologies and waves. We argue that it should exist in realistic higher-dimensional theories as well. Among other things we also briefly outline the relations existing betweenthe low-dimensional models that we have discussed hereand the realistic higher-dimensional ones. This paper develops further some ideas already present in our previous papers. We briefly reproduce here (without proof) their main results in a more concise form and give an important generalization.

Keyword(s): dilaton gravity ; dimensional reduction ; cosmology ; integrable model ; separation of variables ; gravity wave ; supergravity

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