Isometries and Spontaneous Lorentz Violation in General Relativity

Author (Your Name)

Greg Merritt, Colby CollegeFollow

Date of Award

2012

Document Type

Honors Thesis (Open Access)

Department

Colby College. Physics and Astronomy Dept.

Advisor(s)

Robert T. Bluhm

Abstract

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.

Keywords

general relativity, isometries, Lorentz violation

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