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

摘要

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