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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Physics
Year Degree Awarded
2015
Month Degree Awarded
September
First Advisor
David Kastor
Second Advisor
Jennie Traschen
Third Advisor
John Donoghue
Fourth Advisor
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.
DOI
https://doi.org/10.7275/7504405.0
Recommended Citation
Ett, Benjamin, "Exact Solutions in Gravity: A journey through spacetime with the Kerr-Schild ansatz" (2015). Doctoral Dissertations. 493.
https://doi.org/10.7275/7504405.0
https://scholarworks.umass.edu/dissertations_2/493
Included in
Cosmology, Relativity, and Gravity Commons, Elementary Particles and Fields and String Theory Commons