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 that the wave solutions depend on two variables: space and time. They are obtained here both by reducing the moduli space (available because of complete integrability) and by a generalized separation of variables (also applicable to nonintegrable models and to higher-dimensional theories). Among these new wavelike solutions, we find 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 also exist in realistic higher-dimensional theories. Among other things, we also briefly outline the relations existing between the low-dimensional models that we discuss here and the realistic higher-dimensional ones.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 422–452, December, 2007.
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de Alfaro, V., Filippov, A.T. Dimensional reduction of gravity and relation between static states, cosmologies, and waves. Theor Math Phys 153, 1709–1731 (2007). https://doi.org/10.1007/s11232-007-0142-9
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DOI: https://doi.org/10.1007/s11232-007-0142-9