r - qc / 0 30 51 07 v 2 2 3 Ju n 20 03 Vacuum solutions which cannot be written in diagonal form ∗
نویسندگان
چکیده
The vacuum solution ds = dx + x dy + 2 dz dt + lnx dt of the Einstein gravitational field equation follows from the general ansatz ds = dx + gαβ(x) dx dx but fails to follow from it if the symmetric matrix gαβ(x) is assumed to be in diagonal form. KEY: Vacuum solution, Einstein field equation, symmetries, diagonalization
منابع مشابه
ar X iv : g r - qc / 0 31 20 38 v 2 2 0 Ju l 2 00 4 Strings and Branes under Microscope
It is shown that in the standard vacuum 5D Kaluza-Klein gravity there is wormhole-like solutions which look like strings attached to two D-branes. The asymptotical behaviour of the corresponding metric is investigated.
متن کاملiv : g r - qc / 0 30 60 65 v 1 1 6 Ju n 20 03 Cosmology in a Higher - Curvature Gravity
We investigated the cosmology in a higher-curvature gravity where the dimensionality of spacetime gives rise to only quantitative difference, contrary to Einstein gravity. We found exponential type solutions for flat isotropic and homogeneous vacuum universe for the case in which the higher-curvature term in the Lagrangian density is quadratic in the scalar curvature, ξR 2. The solutions are cl...
متن کاملVacuum Solutions Which Cannot Be Written in Diagonal Form *
The vacuum solution ds 2 = dx 2 + x 2 dy 2 + 2 dz dt + ln x dt 2 of the Einstein gravitational field equation follows from the general ansatz ds 2 = dx 2 + g αβ (x) dx α dx β but fails to follow from it if the symmetric matrix g αβ (x) is assumed to be in diagonal form.
متن کامل- qc / 0 20 70 56 v 1 1 5 Ju l 2 00 2 The Mixmaster Universe in Five Dimensions Paul
We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this result within the context of induced matter theory.
متن کاملar X iv : g r - qc / 9 51 20 29 v 2 7 F eb 1 99 6 Perfect - fluid cylinders and walls — sources for the Levi – Civita space – time
The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein’s field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is perio...
متن کامل