Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-09-27
Class.Quant.Grav.27:225024,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, 1 figure
Scientific paper
10.1088/0264-9381/27/22/225024
A study of the lightcone of the G\"odel 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.
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