Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-12-17
Sov.Phys.J. 34 (1992) 781
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages, pdf only; the v.2 is supposed to have more Latex
Scientific paper
Observing the list of compatible second order equations of Absolute Parallelism (AP) found by Einstein and Mayer (for D=4), we have indicated the one-parameter class of equations taking on 3-linear form (when contra-frame density of some weight is in use). Spherically symmetric solutions to these equations are considered, and we try not to add any \delta-sources (ie, $\delta(r)$-sources of unknown nature) during integrations concerned with high symmetry. Using two different ways to fix radius and time, we have found that only non-static solutions (except for trivial one, of course) are possible. If D=5, such solutions, looking like a single wave (or a file of single waves) moving along the radius, could serve as (a base of) an expanding cosmological model. It is interesting that the one coordinate choice used leads to the first order system, which is closely similar to gas-dynamic equations for Chaplygin gas, with solutions being free of gradient catastrophe. On the contrary, the other coordinates used show the possibility of solutions with arising ("weak") singularities (it is still not clear whether the measure of such solutions is not zero).
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