Ozsváth–Schücking metric

In Einstein's theory of general relativity, the Ozsváth–Schücking metric, or the Ozsváth–Schücking solution, is a rotating vacuum solution to the field equations, published by István Ozsváth and Engelbert Schücking in 1962. The paper abstract reads:

An exact solution is given for Einstein's vacuum field equations which is free of singularities, is complete, and has a nonvanishing Riemann tensor. The curvature tensor of this anti-Mach-metric is of the null-type in the Petrov-Pirani-Penrose classification. The singularities and the periodicity structure of the light cone of an arbitrary event in such a universal pure gravitational radiation field are discussed.

In Cartesian coordinates the metric has the form^{[citation needed]}

ds² = − 2[(x² − y²)cos(2t) − 2xysin(2t)]dt² + dx² + dy² − 2dtdz.

This metric stands in contradiction to a statement of Mach's principle by F. Pirani that goes "In the absence of matter, space-time should necessarily be Minkowskian."^[1]

References

1. ^ F. Pirani 1957 Phys. Rev. 105, 1089.

• Ozsváth, I., Schücking, E. (1962). "An anti-Mach metric." Recent developments in general relativity (New York: Pergamon), pp. 339–50.
• Helv. Phys. Acta Suppl. IV, p. 199 (1956).
• E. Cartan, Geometrie des espaces de Rientann, Paris 1951, pp. 260-2.
• A. Lichinerowicz, C. R. Acad. Sci, Paris 246, 893 (1958).
• F. Pirani, Phys. Rev. 105, 1089 (1957).