New singularity and existence of solutions in anisotropic, time-dependent, maximally Gauss-Bonnet extended gravity

Details New singularity and existence of solutions in anisotropic, time-dependent, maximally Gauss-Bonnet extended gravity New singularity and existence of solutions in anisotropic, time-dependent, maximally Gauss-Bonnet extended gravity

Jun 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phdt........19k&link_type=abstract

Ph.D. Thesis Utah State Univ., Logan.

Mathematics

Anisotropy, Cosmology, Einstein Equations, Gravitation Theory, Gravitational Fields, Lagrange Coordinates, Singularity (Mathematics), Space-Time Functions, String Theory, Time Dependence, Time Functions, Unified Field Theory, Curvature, Geodesic Lines, Inversions, Perturbation Theory

Scientific paper

Some unification theories, including superstring theories, suggest spacetimes of higher dimensions than four. We consider the maximally Gauss-Bonnet extended Einstein Lagrangian, commonly known as the Lovelock Lagrangian, as a viable candidate for a gravitational Lagrangian that generalizes Einstein's theory in such higher dimensional spacetimes. In this dissertation, motivated by the success of the Kasner cosmology, we study the diagonal metric, time-dependent, homogeneous cosmology based on the Lovelock Lagrangian. We use the Palatini variation to obtain the field equations from the Lagrangian. The field equations are then integrated to obtain the most general diagonal metric, time-dependent, anisotropic solution. The solutions obtained are not in a desirable form; they are algebraic expressions of a time variable in terms of metric variables whereas we would like to have expressions of the metric variables as functions of a time variable. We prove the theorems regarding the conditions under which this inversion is possible. It is shown that, for certain solutions we found, the second time derivatives of the metric components of the solution, rather than the metric components, diverge, and this forces a certain curvature invariant to diverge. Thus, the singularity behavior of these solutions we found differs from the classical Kasner solution. Perturbative solutions both emerging from and evolving toward a singularity are obtained. The equation of geodesic deviation is solved perturbatively to show that the co-moving coordinates do not break down at a singularity.

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