Honors Students' Abstracts
Conformal Gravity and Related Weyl Tensors as an Alternative to Standard General Relativity
To account for recent discoveries that might contradict Einstein’s General Theory of Relativity, scientists posed the highly debated theory of “dark matter” and “dark energy,” claimed to account for the majority of the Universe. Alternatives to dark energy and dark matter either retain and add to Einstein’s theory or completely stray away from this standard. P. Mannheim and D. Kazanas reject the notion of dark matter/dark energy and propose an explanation for these cosmological puzzles using gravitational equations derived from a geometry proposed by Weyl in the early twentieth century, a complex and previously discarded system largely based on tensors. Mannheim and Kazanas solved these derived equations, a solution which preserved Einstein’s Theory of General Relativity at the smaller scale, but which deviated from it at large galactic distances. This new theory is called Conformal Gravity. Using a Mathematica program developed in collaboration with Dr. G. Varieschi, I have been testing Mannheim and Kazanas’ findings for different coordinate expressions of the line element and the related tensors. As of now, we have found that their results do match those obtained by our Mathematica program. After concluding this testing phase of the project, we will use these results as a basis for applications of Conformal Gravity to modern Cosmology, i.e., to study the nature and evolution of the Universe.