On static and radiative space-times |
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Authors: | Helmut Friedrich |
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Affiliation: | (1) Max-Planck-Institut für Physik und Astrophysik, Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-8046 Garching bei München, Federal Republic of Germany |
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Abstract: | The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain radiativity condition, is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain radiative solution which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their free data is given and non-symmetry properties are discussed. |
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