ar X iv : 0 80 3 . 26 84 v 1 [ gr - q c ] 1 8 M ar 2 00 8 Lev Landau and the problem of singularities in cosmology

ar X iv : 0 71 2 . 38 38 v 3 [ gr - q c ] 3 1 M ay 2 00 8 General Transformation Formulas for Fermi - Walker Coordinates

ar X iv : 0 80 4 . 34 49 v 2 [ gr - q c ] 1 7 M ay 2 00 8 Noether symmetry in f ( R ) cosmology

The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effe...

ar X iv : 0 80 5 . 36 61 v 1 [ m at h . A P ] 2 3 M ay 2 00 8 Boundary singularities of solutions of N - harmonic equations with absorption ∗

Abstract We study the boundary behaviour of solutions u of −∆Nu + |u| u = 0 in a bounded smooth domain Ω ⊂ R subject to the boundary condition u = 0 except at one point, in the range q > N − 1. We prove that if q ≥ 2N − 1 such a u is identically zero, while, if N − 1 < q < 2N − 1, u inherits a boundary behaviour which either corresponds to a weak singularity, or to a strong singularity. Such si...

ar X iv : 0 71 0 . 20 41 v 3 [ gr - q c ] 1 3 M ar 2 00 8 Thin - shell wormholes supported by ordinary matter in Einstein – Gauss – Bonnet gravity

The generalized Darmois–Israel formalism for Einstein–Gauss–Bonnet theory is applied to construct thin-shell Lorentzian wormholes with spherical symmetry. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions.

ar X iv : 0 80 5 . 47 38 v 1 [ he p - th ] 3 0 M ay 2 00 8 U ( 1 ) invariant Membranes and Singularities

A formulation of U(1) symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE’s, as well as some ideas concerning singularities and integrability. Let me start by giving some particular example(s) of a 2-dimensonal (timelike, time periodic) extremal manifold M2 ⊂ R and 3-folds (singularities included) of vanishing mean curvature, in 4...