VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Wave Equations on Black Hole Spacetimes
Last Updated: 2026-02-05 15:54:09
Abstract
Introduction to Lorentzian geometry, to the notion of a black hole, and to the study of linear wave equations on such spacetimes.
Objective
We will learn about the basics of Lorentzian geometry, the geometric framework which incorporates space and time as one geometric entity---spacetime. Then, we will briefly introduce the Einstein equations of General Relativity and study the Schwarzschild and Reissner--Nordström black holes solutions. We will further discuss tools to study linear wave equations on black holes and other spacetimes.
Content
Black holes are among the central theoretical predictions of general relativity which is governed by the celebrated Einstein's equations. The notion of a black hole has a clean mathematical definition, and the concept is already exhibited by the simplest non-trivial solution of the Einstein vacuum equation: the Schwarzschild solution. These “black hole spacetimes” give rise to many natural mathematical problems in the analysis of (hyperbolic) PDE which in turn describe physical phenomena related to black holes. More specifically we will cover the following topics: Basic Lorentzian geometry, the Schwarzschild and Reissner-Nordström black hole, the wave equation on general Lorentzian manifolds, the wave equation on black hole backgrounds. We will also adapt the content to the prior knowledge of the students.
Resources
Literature
Main reference: Lecture Notes of Mihalis Dafermos: https://www.dpmms.cam.ac.uk/~md384/ETH-Nachdiplom-temp.pdf Further references (going beyond the scope of the seminar): - Dafermos, Mihalis, and Igor Rodnianski. "Lectures on black holes and linear waves." Clay Math. Proc 17 (2013): 97-205. (see also arXiv:0811.0354) - Aretakis, Stefanos. "General Relativity". https://www.math.toronto.edu/aretakis/General%20Relativity-Aretakis.pdf - Christodoulou, Demetrios. Mathematical problems of general relativity I. Vol. 1. European Mathematical Society, 2008.
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- ungraded semester performance
Registration & Places
- Signup Start
- 04.01.2021
- Signup End
- 19.02.2021
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| seminar | Wave Equations on Black Hole Spacetimes |
|
2 h weekly |
Offered In
-
-
Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)
-
-
-
-
Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)
-
-