Date of Award
Honors Thesis (Open Access)
Colby College. Physics and Astronomy Dept.
Robert T. Bluhm
General Relativity, or GR, is a theory which describes gravity as a manifestation of the curvature of space and time. While the other three fundamental forces in nature are represented as ﬁeld theories, GR is a geometric theory. In the search for a way to reconcile the ﬁeld theories for the electromagnetic, strong, and weak forces with the gravitational force, a logical place to start is by re-expressing GR as a ﬁeld theory. In doing so, we ﬁnd that the theory contains a number of symmetries. When we solve the equations in GR, we ﬁnd that by choosing certain solutions we break some of the symmetries of the system (through a mechanism known as spontaneous symmetry breaking.) We seek to ﬁnd out how the total number of symmetries, which are represented mathematically as isometries, change for different solutions when we add a vector potential ﬁeld which spontaneously breaks (Lorentz) symmetry. Such a mechanism is thought to occur in higher dimensional theories such as String Theory, and so a better understanding of the mechanism in GR could be useful in later work. We will ﬁnd that the number of symmetries is reduced from 10 to 6 with a time-dependent vacuum solution, which is the same number of symmetries that our actual universe is thought to possess.
general relativity, isometries, Lorentz violation
Recommended CitationMerritt, Greg, "Isometries and Spontaneous Lorentz Violation in General Relativity" (2012). Honors Theses. Paper 653.
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