On Bianchi type-I vacuum solutions inR+R ² theories of gravitation. II. The axially symmetric anisotropic case

Abstract

The field equations following from a LagrangianL(1/L)(−g)^1/2[(1/2)R+l ²(αR _lk R ^lk+βR ²)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,α+3β=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.