General Relativistic Magnetohydrodynamics: Theory and Numerical Simulations

Short course by  Yosuke Mizuno (Goethe University Frankfurt) recorded at IAG/USP - August 13-17, 2018.

 

WEBSITE of lecture notes: https://itp.uni-frankfurt.de/~mizuno/grmhd_2018.html
 
 
Goals:
 
This mini-course aims at  introducing to graduate students and researchers with some previous knowledgement of  magnetohydrodynamics, the basic concepts of special and general relativistic magnetohydrodynamics. These are essential tools to understand astrophysical phenomena related to compact objects like black holes, relativistc jets, etc.
 
 
 
Course description: 
 
This special course will provide an introduction to the mathematical and physical properties of magnetohydrodynamics in relativistic regime. Starting from an 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.
 
 
 
References: 
 
•  Anile, 1990, Relativistic Fluids and Magneto-fluids, Cambridge 
•  Andersson & Comer 2007, Relativistic Fluid Dynamics: Physics for Many 
Different Scales, Living Reviews in Relativity 
•  Font 2008, Numerical Hydrodynamics and Magnetohydrodynamics in General 
Relativity, Living Reviews in Relativity 
•  Rezzolla & Zanotti 2013, Relativistic Hydrodynamics, Oxford