Cosmology, Relativity, and Gravity Commons^™

Characterization Of Extended Uncertainty Principle Black Holes, Juan Uribe, Jonas Mureika

Honors Thesis

Black Holes are special objects as they are at the intersection of Quantum Mechanics and General Relativity. A central tenant of quantum mechanics is the Uncertainty Principle that dictates we cannot know with complete certainty position and momentum at the same time. The Extended Uncertainty Principle introduces a position-related uncertainty correction L_* to account for General Relativity. In a previous paper, a black hole metric associated with the Extended Uncertainty Principle was derived, by modifying the metric function of a Schwarzschild black hole. This metric introduces near-horizon structures that should produce observable effects, such as love numbers, gravitational wave echoes, …

Laplace's Equation In Fractional-Dimension Spaces, Kyle Schoener, Gabriele Varieschi

Honors Thesis

The correct way to model gravity is a question in physics whose answer continues to elude our understanding. One major difficulty is the dark matter problem, which exists due to the mass discrepancy between predicted and measured values in our universe. One possible solution to this problem is Modified Newtonian Dynamics (MOND). MOND is an alternative gravity model that modifies Newtonian Dynamics with the hope to avoid the necessity of dark matter.

Dr. Varieschi has done work connecting MOND to Newtonian Fractional-Dimension Gravity—the application of fractional calculus and fractional mechanics to classical gravitation laws. In this formulation, we can consider …

Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans

Mathematics Faculty Works

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can …