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.