Dimensional reduction of gravity and relation between static states, cosmologies, and waves
- 37 Downloads
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.
Keywordsdilaton gravity dimensional reduction cosmology integrable model separation of variables gravity wave supergravity
Unable to display preview. Download preview PDF.
- 7.H. Stefani et al., Exact Solutions of the Einstein’s Field Equations, Cambridge Univ. Press, Cambridge (2002).Google Scholar
- 8.V. A. Belinskii and V. E. Zakharov, Sov. Phys. JETP, 48, 985 (1978).Google Scholar
- 10.H. Nicolai, D. Korotkin, and H. Samtleben, “Integrable classical and quantum gravity,” in: Quantum Fields and Quantum Space Time (NATO Adv. Sci. Inst. Ser. B. Phys., Vol. 364), Plenum, New York (1997), p. 203; arXiv:hep-th/9612065v1 (1996).Google Scholar
- 13.V. de Alfaro and A. T. Filippov, “Integrable low dimensional theories describing higher dimensional branes, black holes, and cosmologies,” arXiv:hep-th/0307269v1 (2003).Google Scholar
- 14.V. de Alfaro and A. T. Filippov, “Integrable low dimensional models for black holes and cosmologies from high dimensional theories,” arXiv:hep-th/0504101v1 (2005).Google Scholar
- 15.V. de Alfaro and A. T. Filippov, “Black holes and cosmological solutions in various dimensions,” (unpublished).Google Scholar
- 17.A. T. Filippov, “Some unusual dimensional reductions of gravity: Geometric potentials, separation of variables, and static-cosmological duality,” arXiv:hep-th/0605276v2 (2006).Google Scholar
- 18.V. de Alfaro and A. T. Filippov, “Dynamical dimensional reduction,” (unpublished)Google Scholar
- 26.G. D. Dzhordzhadze, A. K. Pogrebkov, and M. C. Polivanov, “On the solutions with singularities of the Liouville equation,” Preprint IC/78/126, ICTP, Trieste (1978).Google Scholar
- 28.A. N. Leznov and M. V. Saveliev, Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems [in Russian], Nauka, Moscow (1985); English transl. (Progr. Phys., Vol. 15), Birkhäuser, Basel (1992).Google Scholar
- 31.K. Stelle, “BPS branes in supergravity,” in: Quantum Field Theory: Perspective and Prospective (NATO Sci. Ser. C. Math. Phys. Sci., Vol. 530), Kluwer, Dordrecht (1999), p. 257; arXiv: hep-th/9803116v2 (1998).Google Scholar