Theoretical and Mathematical Physics

, Volume 153, Issue 3, pp 1709–1731 | Cite as

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

  • V. de AlfaroEmail author
  • A. T. Filippov


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.


dilaton gravity dimensional reduction cosmology integrable model separation of variables gravity wave supergravity 


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© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Dipartmento di Fisica Teorica and INFNTorinoItalia
  2. 2.Accademia delle Scienze di TorinoTorinoItalia
  3. 3.Joint Institute for Nuclear ResearchDubna, Moscow OblastRussia

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