Singularities and rigidity in non-smooth spacetimes

Disciplines

Mathematics (100%)

Keywords

Singularity Theorem, Splitting Theorem, Nonsmooth Spacetime, Mathematical General Relativity, Synthetic energy conditions, Ricci curvature

Abstract

The theory of relativity was put forth by Albert Einstein in the beginning of the 20th century as the correct theoretical-mathematical framework in which to study gravity. Einsteins ingenious observation was that gravity is not a force, but a manifestation of the curvature of the geometry of the spacetime-continuum. Many physically relevant phenomena (e.g. black holes) however necessitate going beyond the classical (smooth) methods of spacetime geometry, hence we will use the recently developed methods of nonsmooth spacetime geometry in order to obtain deeper insights. With the help of these new methods, we aim at generalizing known classical theorems, such as the result regarding gravitational collapse by Roger Penrose (Nobel Prize Physics 2020) or statements regarding the rigidity of certain spacetime scenarios.