Stationary ``Noncanonical'' Solutions of the Einstein Vacuum Field Equations

The paper studies a spacetime endowed with two stationary metrics. The first one is a Riemannian one, called the R-Schwarzschild metric. It satisfies Einstein vacuum field equations, describes correctly the slowdown of clocks in the gravitational field, the orbits of the planets and the perihelion drift. The R-Schwarzschild metric can be seen as the basic texture of the spacetime. All objects having mass are ruled by this Riemannian metric. The second metric, the light-adapted one, is deduced both taking into account the Rosen-type bi-metric compatibility condition and by the preservation of the axiom of the speed of the light limit. This second metric offers the texture of the “light-like” objects. The main “normal” surprise is that this metric can be only the classical Schwarzschild metric. So, a Rosen-type bi-metric universe exists and its properties are in accordance with the experimental physical evidences.

Download Full-text

Exact treatment of time-dependent axisymmetric gravitation

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0042 ◽

1993 ◽

Vol 440 (1910) ◽

pp. 711-715 ◽

Cited By ~ 2

Keyword(s):

Exact Solution ◽

Time Dependent ◽

New Method ◽

Vacuum Field ◽

Axially Symmetric ◽

Field Equations ◽

Canonical Solution ◽

Gravitational Fields ◽

Einstein Vacuum

This paper extends an earlier treatment of time-dependent gravitational fields that are axially symmetric and non-rotating. From a consideration of the canonical solution of the Einstein vacuum field equations previously obtained as an axial expansion, a new method has been found that now provides the exact solution, whenever a certain generative key function X ( t , z ) is known.

Download Full-text

Einstein vacuum field equations with a single non-null Killing vector

General Relativity and Gravitation ◽

10.1007/bf00756909 ◽

1991 ◽

Vol 23 (8) ◽

pp. 861-876 ◽

Cited By ~ 3

Author(s):

E. D. Fackerell ◽

R. P. Kerr

Keyword(s):

Killing Vector ◽

Vacuum Field ◽

Field Equations ◽

Einstein Vacuum

Download Full-text

On the static field in general relativity: II

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100054566 ◽

1978 ◽

Vol 83 (2) ◽

pp. 299-306

Author(s):

Jamal N. Islam

Keyword(s):

Approximation Scheme ◽

Power Series Expansion ◽

Static Field ◽

Vacuum Field ◽

Diagonal Form ◽

Field Equations ◽

Similar Reduction ◽

Functions Of Two Variables ◽

Einstein Vacuum ◽

Diagonal Forms

AbstractSome aspects are considered of the Einstein vacuum field equations for the diagonal form of the general static metric. A power series expansion is considered in which in the first non-trivial order one gets seven equations for four unknowns. This is reduced to a single Poisson equation in which the source is given in terms of a harmonic function and some arbitrary functions of two variables. A similar reduction is carried out in detail for the next non-trivial order. The approximation scheme can be extended to arbitrarily high orders in principle. The connexion of the diagonal form with the Weyl solutions and the merits of the diagonal and non-diagonal forms are briefly discussed. A general solution of one of the field equations is presented.

Download Full-text