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Anisotropic, Time-Dependent Solutions In Maximally Gauss-Bonnet Extended Gravity, T. Kitaura, James Thomas Wheeler

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In an arbitrary number of dimensions, we find the full exact anisotropic, time-dependent, diagonal-metric solutions to maximally Gauss-Bonnet extended gravity theory. This class of theories, for which the lagrangian is an arbitrary linear combination of dimensionally extended Euler forms, is the most general gravitational theory in which the field equations contain no more than second derivatives of the metric.

We show that the space-time exponentially approaches an asymptotic state of constant, anisotropic curvature and prove three theorems concerning two generic types of singularities. The first theorem gives conditions for the existence of Kasner-like curvature singularities. For these the metric diverges …