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A minimal no-radiation approximation to Einstein's field equations

Gerhard Schäfer·Achamveedu Gopakumar
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Abstract

An approximation to Einstein's field equations in Arnowitt-Deser-Misner (ADM) canonical formalism is presented which corresponds to the magneto-hydrodynamics (MHD) approximation in electrodynamics. It results in coupled elliptic equations which represent the maximum of elliptic-type structure of Einstein's theory and naturally generalizes previous conformal-flat truncations of the theory. The Hamiltonian, in this approximation, is identical with the non-dissipative part of the Einsteinian one through the third post-Newtonian order. The proposed scheme, where stationary spacetimes are exactly reproduced, should be useful to construct {\em realistic} initial data for general relativistic simulations as well as to model astrophysical scenarios, where gravitational radiation reaction can be neglected.

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Gerhard Schäfer, Achamveedu Gopakumar. 2003-10-07. A minimal no-radiation approximation to Einstein's field equations. https://doi.org/10.1103/physrevd.69.021501

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