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Wave Zone in General Relativity

Arnowitt, R. and Deser, S. and Misner, C. W. (1961) Wave Zone in General Relativity. Physical Review, 121 (5). pp. 1556-1566. ISSN 0031-899X. doi:10.1103/physrev.121.1556.

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It is shown that in general relativity a "wave zone" may be defined for systems which are asymptotically flat. In this region, gravitational radiation propagates freely, independent of its interior sources, and obeys the superposition principle. The independent dynamical variables of the full theory which describe the radiation are shown to be coordinate invariant in the wave zone and to satisfy the linearized theory's equations there. Thus, the basic properties of free waves in linear field theories (e.g., electrodynamics) are reproduced for the gravitational case. True waves are also clearly distinguished from so-called "coordinate waves." Reduction to asymptotic form (taking leading powers of 1/r ), is not identical to linearization, since, for example, the Newtonian-like 1/r part of the metric begins quadratically in the linear theory's variables. The Poynting vector of the full theory, which measures energy flux in the wave zone, is correspondingly shown to be given by the linearized theory's formula. This Poynting vector is also shown to be coordinate-invariant in the wave zone. All the physical quantities may therefore be evaluated in any frame becoming rectangular sufficiently rapidly. A brief discussion of measurements of the canonical variables in the wave zone is given. The relation between the present work and other treatments of gravitational radiation is examined.

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Deser, S.0000-0001-9285-9434
Additional Information:© 1961 American Physical Society. (Received August 18, 1960) Research supported in part by Wright Air Development Division, Air Research and Development Command, U. S. Air Force, and the Air Force Office of Scientific Research. Research supported in part by National Science Foundation and by Air Force Office of Scientific Research.
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20180724-143009579
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88204
Deposited By: George Porter
Deposited On:24 Jul 2018 22:07
Last Modified:16 Nov 2021 00:24

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