## General Relativity

General Relativity (GR) is Einstein’s geometric theory of gravity. It is different than the other interactions because the gravitational field, the metric, is not a field that propagates on some space-time, it DEFINES the space-time. This makes the gravitational field self-interacting and interacting with matter in a much more complicated way than matter by itself does. For instance, the Lagrangian of the Standard Model is a fourth order polynomial in all matter fields. The Einstein-Hilbert Lagrangian is not even a polynomial. The interaction of geometry and matter is the content of Einstein’s field equations which relates the curvature of geometry to energy density of matter. Classical GR is our best theory of the gravitational interactions but it has its limitations: The celebrated Penrose-Hawking singularity theorems predict its own failure since the field equations become meaningless inside black holes and close to the big bang. Both curvature and energy density diverge, they become singular. This indicates that the theory has been pushed beyond the limits of validity and must be replaced by a more fundamental one.