Diverging and twisting type N solutions of vacuum Einstein equations: an approximative approach

Physics

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Scientific paper

An approximative method to find diverging and twisting type N solutions to the vacuum Einstein equations is considered. The general solution of iteration equations is found. The general metric of a regular spacetime in the first-order approximation is given. It is shown that there exists no regular solution in the second-order approximation. This leads us to the conclusion that there are severe difficulties in considering the vacuum type N solutions as those describing the gravitational radiation from a bounded source. In this paper, the Debney Kerr Schild coordinates are employed and the zero-order approximation is taken to have a particular simple form.

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