Physics
Scientific paper
Jan 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gregr..13...79n&link_type=abstract
General Relativity and Gravitation, Volume 13, Issue 1, pp.79-99
Physics
5
Gravitation Theory
Scientific paper
Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption thatΨ _0 = O(r^{ - 2 - \varepsilon _0 } ), (d/dr)Ψ _0 = O(r^{ - 3 - \varepsilon _0 } ) and (δ/δx A )Ψ _1 = O(r^{ - 2 - \varepsilon _0 } ), wherex A (A = 2, 3) are angular coordinates, they show thatΨ _1 = O(r^{ - 2 - \varepsilon _1 } ), where ɛ1⩽ 2 and ɛ1<ɛ0;< \varepsilon _0 ;Ψ _2 = O(r^{ - 2 - \varepsilon _2 } ), where ɛ2 ⩽ 1 and ɛ1< ɛ1; and Ψ4 and Ψ3 peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumptionΨ _0 = O(r^{ - 3 - \varepsilon _0 } ), (d/dr)Ψ _0 = O(r^{ - 4 - \varepsilon _0 } ), and (δ/δx A )Ψ _0 = O(r^{ - 3 - \varepsilon _0 } ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.
Goldberg Joshua N.
Novak Stephanie
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