Gravity, Geometry, and the Quantum

Abstract

There are various indications that finding a quantum theory of gravity is important for a full understanding of fundamental physics. Loop quantum gravity is one possibility for such a quantum theory. In the following, we explain its origin in a gauge theoretic reformulation of gravity, and its status as a quantum theory of geometry. An overview is given over Einstein’s equations in the quantum theory. As an example for an application of loop quantum gravity, the quantum theory of certain black hole horizons is sketched. We close with an outlook on current research and future challenges.