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General Relativity and Quantum Cosmology, gr-qc
Abstract:
A study of the lightcone of the Gödel universe is extended to the so-called
G\"odel-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
G\"odel metric. The quasi-periodic refocussing of cone generators with
startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the
lightcone of a plane gravitational wave and also found in the G\"odel universe,
is a feature of the whole G\"odel 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.
