Vacuum Solutions Which Cannot Be Written in Diagonal Form *
نویسندگان
چکیده
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.
منابع مشابه
r - qc / 0 30 51 07 v 2 2 3 Ju n 20 03 Vacuum solutions which cannot be written in diagonal form ∗
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
متن کاملElliptic Systems and Material Interpenetration
We classify the second order, linear, two by two systems for which the two fundamental theorems for planar harmonic mappings, the Radó– Kneser–Choquet Theorem and the H. Lewy Theorem, hold. They are those which, up to a linear change of variable, can be written in diagonal form with the same operator on both diagonal blocks. In particular, we prove that the aforementioned Theorems cannot be ext...
متن کاملOn vacuum-vacuum amplitude and Bogoliubov coefficients
Even if the electromagnetic field does not create pairs, virtual pairs lead to the appearance of a phase in vacuum-vacuum amplitude. This makes it necessary to distinguish the inand out-solutions even when it is commonly assumed that there is only one complete set of solutions as, for example, in the case of a constant magnetic field. Then inand out-solutions differ only by a phase factor which...
متن کاملMatching of spatially homogeneous non-stationary space–times to vacuum in cylindrical symmetry
We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces, singularities and Cauchy horizons. The solutions cannot be asymptotically flat and we present evidence that t...
متن کاملar X iv : 0 90 8 . 21 60 v 1 [ gr - q c ] 1 5 A ug 2 00 9 4 D spacetimes embedded in 5 D light - like Kasner universes
We consider spatially homogeneous, anisotropic cosmological models in 5D whose line element can be written as dS 2 = A(u, v)dudv − Bij (u, v)dx i dx j , (i, j = 1, 2, 3), where u and v are light-like coordinates. In the case where Bij is diagonal, we construct three families of analytic solutions to the 5D vacuum field equations RAB = 0 (A, B = 0, 1, 2, 3, 4). Among them, there is a family of s...
متن کامل