Numerical Relativity

Course guarantor:

Josef Schmidt

Lecturer:

Josef Schmidt

Tutor:

Supervisor:

Department of Physics

Synopsis:

The general theory of relativity is currently the most accurate theory of gravity. However, the great complexity of Einstein's equations means that we know only a very few analytically astrophysically relevant solutions. With the development of computers, however, the possibility to simulate spacetimes numerically has emerged, but this requires a significant reformulation of the standard theory. The main part of the course will therefore be devoted to formulating Einstein's equations in a form suitable for solving the initial problem. Specifics of general relativity then include coordinate freedom and the potential presence of physical singularities. In the course, we will also get to applications such as the localization of black holes and the extraction of gravitational waves.

Requirements:

Syllabus of lectures:

Outline of the lectures:

1.3+1 splitting of spacetime

2.ADM formulation of Einstein's equations

3.Initial data and constraint equations

4.Choice of coordinates

5.Sources of gravitational field

6.Numerical methods of solution

7.Localization of black hole horizons

8.Extraction of gravitational waves

9.BSSN formulation of evolution equations

10.Binary black holes

Syllabus of tutorials:

Study Objective:

Study materials:

Recommended references:

[1] T. W. Baumgarte, S. L. Shapiro: Numerical relativity. Solving Einsteins equations on the computer. Cambridge University Press, Cambridge, 2010

[2] T. W. Baumgarte, S. L. Shapiro: Numerical Relativity. Starting from Scratch. Cambridge University Press, Cambridge, 2021

[3] M. Alcubierre: Introduction to 3+1 numerical relativity. Oxford University Press, Oxford, 2012.

[4] E. Gourgoulhon: 3+1 formalism and bases of numerical relativity, lecture notes. arXiv:gr-qc/0703035v1, 2007

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (elective course)