The Metric and Curvature Properties of H-Space

Details The Metric and Curvature Properties of H-Space The Metric and Curvature Properties of H-Space

Nov 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978rspsa.363..445h&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 363, Issue 1715, pp. 445-468

Physics

42

Scientific paper

The space H of asymptotically (left-) shear-free cuts of the I (good cuts) of an asymptotically flat space-time M is defined. The connection between this space and the asymptotic projective twistor space PT of M is discussed, and this relation is used to prove that H is four-complex-dimensional for sufficiently 'calm' gravitational radiation in M. The metric on H-space is defined by a simple contour integral expression and is found to be complex Riemannian. The good cut equation governing H-space is solved to three orders by a Taylor series and the solution is used to demonstrate that the curvature of H-space is always a self dual (left flat) solution of the Einstein vacuum equations.

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