Exact Cosmological Solutions of Nonlinear F (r)-gravity
نویسنده
چکیده
We report on the cited papers refs. 1-18 from the following points of view: What do we exactly know about solutions when no exact solution (in the sense of " solution in closed form ") is available? In which sense do these solutions possess a singularity? In which cases do conformal relations and/or dimensional reductions simplify the deduction? Furthermore, we outline some open questions worth of being studied in future research. 1 Singularity Theorem In ref. 1 the following simple type of singularity theorems was discussed: The coordinates t, x, y, z shall cover all the reals, and a(t) shall be an arbitrary strictly positive monotonously increasing smooth function defined for all real values t, where " smooth " denotes " C ∞-differentiable ". Then it holds Lemma 1: The Riemannian space defined by ds 2 = dt 2 + a 2 (t)(dx 2 + dy 2 + dz 2) is geodesically complete. This fact is well-known and easy to prove; however, on the other hand it holds for the same class of functions a(t) Lemma 2: The Pseudoriemannian space–time defined by ds 2 = dt 2 − a 2 (t)(dx 2 + dy 2 + dz 2) (1) is light–like geodesically complete iff 0 −∞ a(t) dt = ∞ (2) As usual, " iff " denotes " if and only if ". The proof is straightforwardly done by considering light–like geodesics in the x−t-plane. So, one directly concludes 1
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تاریخ انتشار 1998