SHORT Course: Topics in General Relativity II

Wednesday 17 Jun 2026, 15:45 → Monday 22 Jun 2026, 10:45 Europe/Rome

Aurora Building-Main Lecture Hall (GSSI)

Lecturer
Flavio Rossetti (GSSI) flavio.rossetti@gssi.it 

Timetable and workload
Lectures: 8 hours

Course content
The course will focus on the analysis of the wave equation on black hole spacetimes, motivated by the hyperbolic nature of the Einstein equations. First, basic notions of Lorentzian geometry will be introduced, so to provide a covariant definition of the wave operator on general spacetimes. After discussing the main properties of wave solutions on curved backgrounds, black hole spacetimes will be introduced. The last part of the course will revolve around the analysis of linear waves on Schwarzschild black hole exteriors, via physical-space methods. The course will be intended for a broad audience. Some exposure to the analysis of partial differential equations (as for instance the material covered in the first-semester courses at GSSI) will be assumed.

Lecture 1, June 17, 15:45 - 17:15: 

Lorentzian geometry and causality

Lecture 2, June 18, 10:45 - 12:15: 

The wave equation on curved backgrounds

Lecture 3, June 19, 09:00 - 10:30: 

Black hole spacetimes

Lecture 4, June 22, 09:00 - 10:30: 

The wave equation on Schwarzschild black holes (Redshift effect, uniform boundedness of solutions, …)

Related short courses
Topics in General Relativity 
References
The geometry and analysis of black hole  spacetimes in general relativity, M. Dafermos, ETH Nachdiplom lectures, 2013