Dimensional Reduction of Gravity and Relation between Static States, Cosmologies and Waves

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.

28 pages, Appendix and some new material in Sections 2 and Section 4 has been added, misprints corrected and some editing has been done

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Cited by in corpus (6)

• On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology
• Multi-exponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models
• Integrals of equations for cosmological and static reductions in generalized theories of gravity
• Unified description of cosmological and static solutions in affine generalized theories of gravity: vecton - scalaron duality and its applications
• A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations
• On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron