The lightcone of Gödel-like spacetimes

Abstract

A study of the lightcone of the Gödel universe is extended to the so-called Gödel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces is defined by metrics of the form $d{s}^2=-(dt+H(x)dy{)}^2+D^2(x)d{y}^2+d{x}^2+d{z}^2$, 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.

19 pages, 1 figure

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Cited by in corpus (2)

• Symmetries of geodesic motion in Gödel-type spacetimes
• Noether symmetries of the minimal surface Lagrangian for Gödel-type spacetimes