MATH-530 / 5 credits

Teacher: Moschidis Georgios

Language: English

## Summary

This course will serve as a basic introduction to the mathematical theory of general relativity. We will cover topics including the formalism of Lorentzian geometry, the formulation of the initial value problem for the Einstein equations and applications on the global structure of the spacetime.

## Keywords

General relativity; Lorentzian geometry; Einstein field equations; non-linear wave equations; initial value problem

## Required courses

The language of the course "Introduction to differentiable manifolds" (MATH-322) will be heavily used. A solid foundation in analysis (including measure theory and functional analysis) will also be necessary. The students should also have attended at least an introductory course in partial differential equations.

## Recommended courses

Introductory courses in Riemannian geometry and evolution PDEs would be helpful, but not necessary.

## Important concepts to start the course

Differentiable manifold, tensors, partial differential equations

## Learning Outcomes

By the end of the course, the student must be able to:

• Use the language of Lorentzian geometry effectively.
• Define the main concepts associated to the initial value problem formulation for the Einstein equations.
• Use the above notions and the basic PDE techniques introduced in the course to solve problems.
• Prove the main theorems appearing in the course.

## Transversal skills

• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking
• Access and evaluate appropriate sources of information.

## Teaching methods

2h lectures + 2h exercises

## Expected student activities

Attending lectures and solve problems sheets; interacting in class; revise course content.

## Assessment methods

Final exam.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux
étudiants concernés.

## Supervision

 Office hours Yes Assistants No Forum No

No

## Bibliography

We will follow closely the exposition of the following two books:

Wald, Robert; General relativity, The University of Chicago Press, 1984

Ringström, Hans; The Cauchy problem in General relativity, ESI Lectures in Mathematics & Physics, 2009.

## Notes/Handbook

Written notes will be provided.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Introduction to general relativity
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Introduction to general relativity
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Introduction to general relativity
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 MAA331 9-10 10-11 MAA331 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Friday, 8h - 10h: Lecture MAA331

Friday, 10h - 12h: Exercise, TP MAA331