Cohomology theories of spacetimes

Abstract

[en] Recently, non-standard de Rham cohomologies with causally restricted supports have proven to be useful in ongoing theoretical physics research. In this work, we present them starting from the most elementary notions of cohomology in manifolfds and spacetime, thereby offering an overview of de Rham cohomology and an introduction to Lorentzian manifolds and their causal structure. We also characterize these cohomologies in globally hyperbolic spacetimes, exhibiting isomorphims with the standard de Rham cohomologies and providing examples of computation for some well-known physical models of the spacetime.