Eigenschaften singularitätenfreier,statischer, zentralsymmetrischer Lösungen gewisser Gravitationsfeldgleichungen 4. Ordnung |
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| Authors: | H-J Schmidt B Fiedler M Günther |
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| Abstract: | FIEDLER and SCHIMMING (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by TREDER , admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = o (r radius), can now be extended to intervals o ≦ r ≦ α with arbitrarily large α , using the abstract theorem on inverse functions. Further it is proved that the Schwarzschild metrics are in a certain sense the only solutions of the above equations that are analytic, asymptotically flat, static and centrally symmetric around r = +∞. |
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