Existence and Uniqueness of Solutions of an Einstein-Maxwell PDE System

Authors

Toby Aldape, Lewis and Clark College

Abstract

We consider a nonlinear coupled system of partial differential equations with asymptotic boundary conditions which is relevant in the field of general relativity. Specifically, the PDE system relates the factors of a conformally flat spatial metric obeying the laws of gravity and electromagnetism to its charge and mass distributions. The solution to the system is shown to be existent, smooth, and unique. While the discussion of the PDE assumes knowledge of physics and differential geometry, the proof uses only the PDE theory of flat space.

Author Bio

Toby Aldape was born in 1999 in La Grande, Oregon, and moved to Portland, Oregon in 2013. He has studied undergraduate mathematics at Eastern Oregon University, Portland State University, and Lewis and Clark College. Recently, he graduated from Wilson High School and spent a summer doing research with Noah Benjamin, Tatyana Benko, and Professor Iva Stavrov of Lewis and Clark College. He took a year off from school and will soon be studying at the University of Colorado, Boulder.

Faculty Sponsor

Iva Stavrov

Recommended Citation

Aldape, Toby (2017) "Existence and Uniqueness of Solutions of an Einstein-Maxwell PDE System," Rose-Hulman Undergraduate Mathematics Journal: Vol. 18: Iss. 1, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/10