Mathematical Problems in General Relativity and Black Holes
Abstract
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Next lectures
04.12.2024, 11:00 (E2 10 (Leon-Lichtenstein))
11.12.2024, 11:00 (E2 10 (Leon-Lichtenstein))
18.12.2024, 11:00 (E2 10 (Leon-Lichtenstein))
08.01.2025, 11:00 (E2 10 (Leon-Lichtenstein))
15.01.2025, 11:00 (E2 10 (Leon-Lichtenstein))
22.01.2025, 11:00 (E2 10 (Leon-Lichtenstein))
29.01.2025, 11:00 (E2 10 (Leon-Lichtenstein))
05.02.2025, 11:00 (E2 10 (Leon-Lichtenstein))
The goal of this course is to give the audience an idea what kinds of mathematical problems are being studied in general relativity (GR), along with some intuition for these problems.
In the first part of the course, I will introduce the basic concepts and notions of GR.
In the second and main part of the course, I will descend to spherical symmetry (which has the advantage of removing many of the technical difficulties one typically encounters in GR while still allowing for a rich variety of phenomena), give a completely self-contained development of the theory in spherical symmetry, and prove the spherically symmetric analogues of some of the more recent advances in the field.
In the last part of the course, if enough interest remains, I will then give an introduction to some of the actual methods used when studying GR without symmetry.
Keywords
general relativity, initial value problem, black hole formation, black hole stability, cosmic censorship conjectures
Prerequisites
Basic familiarity with Differential Geometry will be helpful but not necessary. Familiarity with PDE will also be helpful but even less necessary.
Audience
People with an interest in what relativity is about
