Geodesic
Dimensional reduction of gravity and relation between static states,
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 422-452

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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.
Keywords: dilaton gravity, dimensional reduction, cosmology, integrable model, separation of variables, gravity wave, supergravity. 
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     author = {V. De Alfaro and A. T. Filippov},
     title = {Dimensional reduction of gravity and relation between static states,},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a7/}
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V. De Alfaro; A. T. Filippov. Dimensional reduction of gravity and relation between static states,. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 422-452. http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a7/