## Doctoral Dissertations

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#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Physics

2015

September

David Kastor

Jennie Traschen

John Donoghue

Floyd Williams

#### Subject Categories

Cosmology, Relativity, and Gravity | Elementary Particles and Fields and String Theory

#### Abstract

The Kerr-Schild metric ansatz can be expressed in the form $g_{ab} = \gbar_{ab}+\lambda k_ak_b$, where $\gbar_{ab}$ is a background metric satisfying Einstein's equations, $k_a$ is a null-vector, and $\lambda$ is a free parameter. It was discovered in 1963 while searching for the elusive rotating black hole solutions to Einstein's equations, fifty years after the static solution was found and Einstein first formulated his theory of general relativity. While the ansatz has proved an excellent tool in the search for new exact solutions since then, its scope is limited, particularly with respect to higher dimensional theories. In this thesis, we present the analysis behind three possible modifications. In the first case a spacelike vector is added to the ansatz, and we show that many, although not all, of the simplifications that occur in the Kerr-Schild case continue to hold for the extended version of the ansatz. In the second case we look at the Kerr-Schild ansatz in the context of higher curvature theories of gravity; specifically Lovelock gravity which organizes terms in the Lagrangian in such a way that the theory is ghost-free and the equations of motion remain second order. We find that the field equations reduce, in a similar manner as in the Kerr-Schild case, to a single equation of order $\lambda^p$ for unique vacuum theories of order $p$ in the curvature. Finally, we investigate the role of the Kerr-Schild ansatz in the context of Kaluza-Klein gravity theories.

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