The lightcone of Gödel-like spacetimes

Abstract

Abstract.A study of the lightcone of the Gödel universe is extended to the socalled Gödel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces is defined by metrics of the form ds 2 = −(dt+H(x)dy) 2 +D 2 (x)dy 2 +dx 2 +dz 2 , together with the requirement of spacetime homogeneity, and includes the Gödel metric. The quasi-periodic refocussing of cone generators with startling lens properties, discovered by Ozsváth and Schücking for the lightcone of a plane gravitational wave and also found in the Gödel universe, is a feature of the whole Gödel family. We discuss geometrical properties of caustics and show that (a) the focal surfaces are two-dimensional null surfaces generated by non-geodesic null curves and (b) intrinsic differential invariants of the cone attain finite values at caustic subsets.

Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes

“…[32] on the solution of lightlike geodesic equations. Afterwards, Dautcourt [33] studied the lightcone of the Gödel-type metrics by considering only the lightlike case. It is given a complete discussion for timelike and null geodesics of Gödel-type spacetimes by Calvão et al [34] and Gleiser et al [35].…”

Symmetries of geodesic motion in Gödel-type spacetimes

“…They have generalized the work of Kajari et al [20] on the solution of lightlike geodesic equations. Recently, Dautcourt [21] considered only the lightlike case, and studied the lightcone of the Gödel-type metrics. Some spacetime symmetry properties of the original Gödel metric and Gödel-type spacetimes (see refs.…”