Fields Academy Shared Graduate Course: Self-Similarity and the Einstein Vacuum Equations
Description
Registration Deadline: Janaury 18th, 2025 (for students taking the course for credits)
Instructor: Professor Yakov Shlapentokh-Rothman, University of Toronto
Course Date: January 5th - April 1st, 2026
Mid-Semester Break: February 16th - 20th, 2026
Lecture Time: Mondays, 3:00 PM - 5:00 PM | Wednesday, 3:00 PM - 4:00 PM (ET)
Office Hours: TBA
Registration Fee:
- Students NOT Taking the Course for Credits: Free
- Students Taking the Course for Credits:
- Students from our Principal Sponsoring & Affiliate Universities: Free
- Other Students: CAD$500
Capacity Limit: TBA
Format: Hybrid Delivery
- In-Person: Room 210, Fields Institute
- Online: via Zoom
Course Description
This course is cross-listed for the Thematic Program on Shocks and Singularities: Nonlinear evolution equations in physical and life sciences (January-June 2026) and the Shared Graduate Courses Program.
This class will give on overview of self-similarity and naked singularities for the Einstein equations.
Topics to be covered may include Christodoulou's naked singularities for the spherically symmetric Einstein-scalar field system, Singh's study of the wave equation on Christodoulou's naked singularity background, introduction to the double-null gauge and the characteristic initial value problem, Fefferman–Graham theory and the asymptotically self-similar regime for the Einstein vacuum equations, and twisted self-similarity and naked singularities for the Einstein vacuum equations.
Schedule
| 15:00 to 17:00 |
Lecture 01 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 02 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 03 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 04 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 05 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 06 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 07 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 08 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 09 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 10 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 11 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 12 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 13 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 14 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 15 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 16 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 17 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 18 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 19 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 20 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 21 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 22 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 17:00 |
Lecture 23 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
| 15:00 to 16:00 |
Lecture 24 | Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman, University of Toronto |
