Wednesday, February 27, 2013

1302.6372 (Alexandre T. Filippov)

Unified description of cosmological and static solutions in affine
generalized theories of gravity: vecton - scalaron duality and its

Alexandre T. Filippov
We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton - vecton gravity field theories (DVG). The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with essentially nonlinear coupling to the dilaton gravity. We emphasize that in DVG the vecton field can be consistently replaced by a new effectively massive scalar field (scalaron) with an unusual coupling to dilaton gravity (DG). With this vecton - scalaron duality, one can use methods and results of DG coupled to scalars (DGS) in more complex dilaton -scalaron theories (DSG) equivalent to DVG. We present the DVG models derived by reductions of multidimensional affine theories and construct one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge and with essentially different parameters. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories as well as in general one-dimensional DGS models. We focus on general and global properties of the models, looking for integrals and studying the structure of the space of solutions. In integrable case, it can be usefully visualized by drawing a `topological portrait' resembling the phase portraits of dynamical systems and simply visualizing global properties of static and cosmological solutions, including horizons, singularities, etc. For analytic approximations we also propose an integral equation well suited for iterations.
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