Understand
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.