Static central-symmetric solutions of the Stephenson equations

The Stephenson's generalized field equations are considered in this work. Static central-symmetric solutions are obtained in an explicit form. It is argued that in the presence of a non-linear 4-curvature correction to the gravitational field's Lagrangian density in the form of α√xi-R+β, the gravitational equations are satisfied by the Schwarzschild-like solution. The possibility is studied of obtaining solutions for a Lagrangian density in the form of L=R2. (author)