István Ozsváth

The finite rotating universe

Abstract We construct on the Lie group R × S3 a left invariant metric, which satisfies the Einstein field equations with incoherent matter. We call the Riemannian space M4, obtained this way, the Finite Rotating Universe, since the normal subgroup S3 constitutes the (finite) space sections of M4, and the matter rotates. We discuss the geometry of M4 and its relation to one version of Machs principle.

Plane‐fronted gravitational and electromagnetic waves in spaces with cosmological constant

Plane‐fronted waves in spaces with nonzero cosmological constant are studied. In particular their complete classification, which depends essentially on the sign of the cosmological constant and that of some second‐order invariant determined by the congruence of null rays, is provided.

NEW HOMOGENEOUS SOLUTIONS OF EINSTEIN'S FIELD EQUATIONS WITH INCOHERENT MATTER OBTAINED BY A SPINOR TECHNIQUE

Einsteins field equations with incoherent matter are solved for the case of homogeneous spacetime, i.e., for metrics allowing a four parametric simply transitive group of motions. Two families of new solutions are obtained by use of a spinor technique. As a special result a proof emerges for Godels theorem, which states that there exist only two homogeneous solutions of Einsteins field equations with incoherent matter and rigid rotation, namely the Godel cosmos and the Einstein static universe.

Dust‐Filled Universes of Class II and Class III

I construct on the Lie group R × H3 two different families of left‐invariant metrics which satisfy the Einstein field equations with incoherent matter, calling the Riemannian spaces M4, obtained this way, Class II and Class III universes. We discuss the geometry of these universes.

Gödel’s trip

We discuss the geometrical light cone structure in Godel’s rigidly rotating cosmos and correct a picture in the standard literature.

Spatially Homogeneous World Models

We obtain the field equations of Einstein for spatially homogeneous spaces as the Euler‐Lagrange equations of a variational problem. We write these equations in Hamiltonian form and regularize them. In this way, we obtain a class of solutions without rotations. We derive, in particular, the Lagrangian function for the rotating model with the S3 group first computed by Godel. We suggest that the corresponding Hamiltonian equations can be regularized.

Pressure as a source of gravity

The active mass density in Einsteins theory of gravitation in the analog of Poissons equation in a local inertial system is proportional to

Approaches to Gödel's rotating universe

\rho+3p/c^2

Active mass under pressure

. Here

An embedding problem

\rho