The aim of the course is to present the Cauchy problem in general relativity. The course will roughly follow the lecture notes

Cauchy problems for the Einstein equations: an Introduction

https://homepage.univie.ac.at/piotr.chrusciel/teaching/Cauchy/Roscoff.pdf

We will cover

• The general relativistic constraint equations

• Local and global solutions

• Various methods of solving the constraint equations

Background: General relativity is one of the central current topics of research in physics. There are several gravitational-wave candidates observed daily by the gravitational wave observatories. The increase of precision of quantum photonics will allow shortly tests of interplay of quantum physics and general relativity. Mathematical general relativity is the theory which provides an appropriate mathematical framework for such studies, and the Cauchy problem lies at the heart of all such studies. The aim of these lectures is to provide students a solid background to current research in this area.

Exam: The student will have the choice to write a short memoir on an advanced topic mutually agreed with the lecturer, or to pass a viva where he will asked to present a randomly chosen topic out of a list of topics provided before hand.

Prerequisites: Differential geometry, some GR.

Registration: https://www.wjx.top/vm/OlVbo5t.aspx#