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On static spherically symmetric solutions of the Bach-Einstein gravitational field equations

H. -J. Schmidt
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Abstract

For field equations of 4th order, following from a Lagrangian `Ricci scalar plus Weyl scalar', it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = 0 and r = infinity resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme.

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H. -J. Schmidt. 2001-05-28. On static spherically symmetric solutions of the Bach-Einstein gravitational field equations. https://arxiv.org/abs/gr-qc/0105107

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