A Spinor approach to general relativity - INSPIRE

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A Spinor approach to general relativity

R. Penrose

Jun, 1960

31 pages

Published in:

Annals Phys. 10 (1960) 171-201

DOI:

10.1016/0003-4916(60)90021-X

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Abstract: (Elsevier)

A calculus for general relativity is developed in which the basic role of tensors is taken over by spinors. The Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten. It is shown that the curvature of empty space can be uniquely characterized by a totally symmetric four-index spinor which satisfies a first order equation formally identical with one for a zero rest-mass particle of spin two. However, the derivatives used here are covariant, so that on iteration, instead of the usual wave equation, a nonlinear “source” term appears. The case when a source-free electromagnetic field is present is also considered. (No quantization is attempted here.)

References(12)

Figures(0)

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