Geometric Analysis, Wave Optics, and Geometric Gravity Models

Duke University, Durham NC

Investigators

Abstract

Abstract Award: DMS-0707003 Principal Investigator: Arlie O. Petters The goal of this research project is to develop a mathematical theory of the shadow patterns cast in the cosmos by the action of gravity on light. The project aims to characterize the pointwise total magnification and magnification cross section functions of these shadow patterns, both in the geometric and wave optics limits for certain key gravity models. This study requires a geometric analysis of caustic singularities, diffraction integrals, and asymptotics in a curved spacetime setting. The proposed research would lay a platform for generalization a study of shadow patterns to arbitrary Lorentzian manifolds, which in turn would lead to a new exploration in Lorentzian geometry. The findings will also yield a detailed gravitational lensing comparison of current key geometric gravity models like general relativity, PPN models, and braneworld gravity, allowing for predictions that may test these gravity models. Shadow patterns are all around us. We drive through them on the way to work and swim among them in pools. Similar patterns are also cast throughout the universe by the gravitational fields of stars, galaxies, black holes, dark matter, and dark energy. Perhaps even more mysterious is that these shadow patterns are connected with one of the profound questions about the nature of our physical world -- namely, whether physical space has more than the familiar three spatial dimensions of length, width, and height. This research will employ gravity's cosmic shadow patterns to explore the nature of black holes and dark matter, and the dimensionality of physical space. The work will also formulate predictions that test Einstein's general theory of relativity and other gravity models. The project is interdisciplinary and creates a synergistic interaction between mathematics, physics, and astronomy.