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Conference Paper

Self-consistent solutions for low-frequency gravitational background radiation


Dautcourt,  G.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Dautcourt, G. (1997). Self-consistent solutions for low-frequency gravitational background radiation. In T. Piran (Ed.), Marcel Grossmann Meeting on General Relativity. Singapore [u.a.]: World Scientific.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5A56-B
We study in a Brill-Hartle type of approximation the back-reaction of a superposition of linear gravitational waves in an Einstein-de Sitter background up to the second order in the small wave amplitudes $h_{ik}$. The wave amplitudes are assumed to form a homogeneous and isotropic stochastic process. No restriction for the wavelengths is assumed. The effective stress-energy tensor $T^{e}_{\mu\nu}$ is calculated in terms of the correlation functions of the process. We discuss in particular a situation where $T^{e}_{\mu\nu}$ is the dominant excitation of the background metric. Apart from the Tolman radiation universe, a solution with the scale factor of the de Sitter universe exists with $p = -\rho$ as effective equation of state.