  In this master thesis, the Frobenius power series method is used to find
spherically symmetric and static vacuum solutions to quadratic and cubic
gravitational actions, representing quantum corrections to the Einstein-Hilbert
action. After a motivation to the topic and an introduction, the power series
solutions are presented. After recovering the results for the quadratic action
of Stelle and collaborators, we found that when the Weyl cubic operator is
present, the (2,2) family of solutions is still present while the
Schwarzschid-de Sitter-like (1,-1) is not.
