Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
arXiv:1204.0291
Abstract
In the first part of this thesis, Kerr-Schild metrics and extended Kerr-Schild metrics are analyzed in the context of higher dimensional general relativity. Employing the higher dimensional generalizations of the Newman-Penrose formalism and the algebraic classification of spacetimes based on the existence and multiplicity of Weyl aligned null directions, we establish various geometrical properties of the Kerr-Schild congruences, determine compatible Weyl types and in the expanding case discuss the presence of curvature singularities. We also present known exact solutions admitting these Kerr-Schild forms and construct some new ones using the Brinkmann warp product. In the second part, the influence of quantum corrections consisting of quadratic curvature invariants on the Einstein-Hilbert action is considered and exact vacuum solutions of these quadratic gravities are studied in arbitrary dimension. We investigate classes of Einstein spacetimes and spacetimes with a null radiation term in the Ricci tensor satisfying the vacuum field equations of quadratic gravity and provide examples of these metrics.
Ph.D. thesis, defended under the original title "General Relativity in Higher Dimensions"
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