Applications of Exterior Algebra in Physics: frame dragging and analogue models of gravity

• Grant number: 18/00202-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): March 01, 2018
• Effective date (End): August 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Maurício Richartz
• Grantee: Eduardo Leme Chica
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated research grant: 13/09357-9 - Physics and geometry of spacetime, AP.TEM

Abstract

Exterior Algebra and differential forms have several applications in Mathematics and Physics, allowing a simpler and more concise description of Maxwell's electromagnetism and Einstein's General Relativity. From fundamental mathematical concepts, like the definitions of manifolds and tensors, this undergraduate research project proposes a detailed and mathematically rigorous study of differential forms. Our end goal is to apply the concepts learned to two different systems: in electromagnetism and in the frame dragging effect of Lense-Thirring. (AU)