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

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

2001-05-28

arxiv.org/abs/gr-qc/0105107v1

Astron.Nachr. 306 (1985) 67-70

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX, no figure

Scientific paper

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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