General Relativistic Magnetohydrodynamics


Instructuor: Yosuke Mizuno
Affiliation: Goethe University Frankfurt

Class hours: 2pm-4pm from August 13th to 17th

1. Couse description:

Magnetohydrodynamics is a successful framework to describe the dynamics of plasma in the universe. This special course will provide an introduction to the mathematical and physical properties of magnetohydrodynamics in relativistic regime. Starting from a introduction and motivation of relativistic astrophysics, the equations of magnetohydrodynamics in Newtonian regime will be overviewed. The course will also discuss the numerical technique for solving the magnetohydrodynamic equations. After overview of basic concept of special and general relativity, the equations of general relativisitc magnetohydrodynamics will be derived and their most important properties will be discussed. The final part of the course will deal with the application of special and general relativistic magnetohydrodynamics to astrophysical problems.

2. Text:

None required. Lecture note will be posted on my website before the subject.

3. References:

(1) Anile, 1990, "Relativistic Fluids and Magneto-fluids", Cambridge
(2) Andersson & Comer 2007, "Relativistic Fluid Dynamics: Physics for Many Different Scales", Living Reviews in Relativity
(3) Font 2008, "Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity", Living Reviews in Relativity
(4) Rezzolla & Zanotti 2013, "Relativistic Hydrodynamics", Oxford

4. Teaching method:

This course will go mainly with classroom lectures and discussion.

Lecture Notes

Ch. 0: Intrudction [Key] [PDF]

Ch. 1: Relativistic Astrophysics and Magnetohydrodynamcis [Key] [PDF]

Ch. 2: Numerical Methods for Solving MHD [Key] [PDF]

Ch. 3: Essence of Special and General Relativity [Key] [PDF]

Ch. 4: 3+1 Form of General Relativistic MHD Equations [Key] [PDF]

Ch. 5: Applications of General Relativistic Magnetohydrodynamics [Key] [PDF]
(Note: most of movies are taken out due to large file size.)


Yosuke Mizuno