Mathematics of Spacetime: A Guided Tour Through The Underlying Differential Topology and Differential Geometry

Abstract

Background in General Relativity (e.g. black holes, wormholes, or spacetime models in general) is needed to comprehend more recent efforts around understanding quantum phenomena like entanglement (e.g. >>It from qubit<< as well as >>ER = EPR<<). The former in turn requires a lot of knowledge from differential topology and differential geometry. While this knowledge is available in very good mathematics textbooks, it is scattered i.e. quite a bunch of sources need to be consulted to acquire it. The goal of this contribution is to provide the major background in a single place; in this sense, this contribution is some sort of guided tour through the corresponding literature.