Geometric Conditions of Hypersurface Deformations for Canonical Gravity Theories
Open Access
Author:
Shah, Aiden
Area of Honors:
Physics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Martin Bojowald, Thesis Supervisor Richard Wallace Robinett, Thesis Honors Advisor
Keywords:
gravity general relativity geometric canonical
Abstract:
Traditionally, canonical computations do not include lapse and shift functions inside of the Poisson brackets, as they do not change the equations of motion at first order. When working with theories that have higher order time derivatives, one needs to include the lapse and shift inside the Poisson brackets as they do add additional terms to the equations of motion. However, there still exists an ambiguity as to whether the lapse and shift should be inside or outside the brackets. We investigate if the canonical methods can describe a geometric theory. We compute the phase space dependence of the hypersurface deformation by computing the lapse and shift inside the Poisson brackets. We use the geometric formulation to derive conditions placed on the canonical formulation. We find that the canonical formulation, when it considers the phase space dependence of the lapse and shift and the deformation of the normal vector, leads not only to the sought after full consistency with the gauge functions inside the brackets, but also a method to obtain new modified gravity theories altogether.
