Anisotropic, time-dependent solutions in maximally Gauss-Bonnet extended gravity

Authors

T. Kitaura
James Thomas Wheeler, Utah State UniversityFollow

Document Type

Article

Journal/Book Title/Conference

Nuclear Physics B

Volume

355

Issue

1

Publication Date

5-13-1991

First Page

250

Last Page

277

Abstract

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 ast^Pi where ∑p_i = 2k_max- 1 and k_max is the highest power of the curvature in the lagrangian. Other critical point singularities can arise from the polynomial nature of the theory. The remaining theorems demonstrate that the generic solution is extendible at all of these other critical points and that the generic critical points occur at moments of external volume density of space-time. We give an explicit coordinate transformation which produces a smooth extension through the critical point. The space-time may therefore alternately expand and contract for many cycles before expanding forever or contracting to a singularity. Many particular cases are treated in detail including several power series solutions, the generalized Kasner solution to general relativity with or without cosmological constant, the perturbative solution for quadratic string gravity, and five-dimensional extended gravity.

Comments

Published by Elsevier in Nuclear Physics B. Author preprint is deposited in KEK Information Service System and is available for download through link above.

Recommended Citation

Takayuki Kitaura, James T. Wheeler, Anisotropic, time-dependent solutions in maximally Gauss-Bonnet extended gravity, Nuclear Physics B, Volume 355, Issue 1, 13 May 1991, Pages 250-277, ISSN 0550-3213, 10.1016/0550-3213(91)90312-L.