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Date of Award
2026
Document Type
Restricted Thesis: Campus only access
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Dr. Jeremy LeCrone
Abstract
Physical laws should not depend on how we choose to describe the world. In this talk, we explore the principle of general covariance: the idea that the laws of physics must remain unchanged under arbitrary coordinate transformations—no matter how “bad” our coordinates are. Starting from this requirement, we are naturally led to the language of differential geometry, where geometry replaces force as the fundamental description of gravity. We introduce curvature as the obstruction to flatness, and show how the full Riemann tensor encodes detailed directional information about spacetime. However, for physics, not all of this information is needed. By taking appropriate contractions, we arrive at the Ricci tensor, which captures how volumes of freely falling matter evolve. Finally, we distill this further into the Ricci scalar, a single quantity representing the average curvature at a point. This progression reveals a central idea of general relativity: gravity is not a force acting in spacetime, but a manifestation of the geometry of spacetime itself.
Recommended Citation
Mascarell, Mariona Giner, "The Geometry of Gravity" (2026). Honors Theses. 1968.
https://scholarship.richmond.edu/honors-theses/1968
Comments
Please Note: This honors thesis has been permanently restricted and is not available for download.