The gravitational field in the wave zone. I: The radiating terms of the metric tensor
[For part II, see the following review.] We consider an asymptotically flat space-time generated by a perfect fluid source of compact spatial support. Using the de Donder gauge conditions, the Einstein equations are reduced to a new form of Poisson- type equations. A formal iterative scheme is set up to solve these equations by expanding the components of the metric tensor in powers of \(c^{-1}\). The coefficient of each power of \(c^{-1}\) depends on the asymptotically retarted time u and x, y, z and satisfies a Poisson-type equation. Assuming asymptotic flatness the solution is carried out in the first orders. The results are explicit expressions of the metric up to order \(c^{-4}\) in terms of the source functions. These expressions hold over all space-time. A further expansion in powers of \(r^{-1}\) gives the first terms of the metric that contribute to gravitational radiation.
scientific article; zbMATH DE number 4011387
scientific article