On guage conditions in the theory of week gravitational waves

Details On guage conditions in the theory of week gravitational waves On guage conditions in the theory of week gravitational waves

Jun 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976race.conf.....g&link_type=abstract

Relativistic Astrophysics and Gravitational Experiment. Collection of scientific works. Minsk 1976, Istitute of Physics of the B

Astronomy and Astrophysics

Astrophysics

1

Weak Gravitational Fields, Linearized Einstein Equations, Weak Waves, Types Of Gravitational Fields, Gayge Conditions, Cauchy Problem

Scientific paper

The authors examine week gravitational waves and gauge conditions for them in week external gravitational fields and on arbitrary curved spacetime. The linearized Einstein equations are considered with additional conditions, corresponding to Cauchy initial problem, such that Cauchy data contain 4 unknown functions of 3 variables. Then the gravitational field will have 2 degrees of freedom (as in the case of exact Einstein equations). Such data will be satisfied in a limited class of metrics, which should be found. The authors found 3 restraint conditions for such metrics, which could lead to other restraints inside every particular case after the satisfaction of the compatibility conditions. In the second case the trace of gravitational field is null. The main results are as follows: The sufficient and necessary condition fоr the satisfaction of a part of the restraint conditions are found; In type N, III gravitational fileds the gauge vector U is isotrope and coincides with the Debeve vector. In type O gravitational fields the gayge vector could be covariant-constant of arbitrary norme, or a field of convergent directions (b=const). In a filled world the case II could be realised for metrics with Weyl tensor of types O,N,III. One of the cases suppose the apartenenece of the metric to equidistant spaces. A particular example of another cases are the gravitational fields in the Friedman world. References: 4

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