Magnetohydrodynamics In 4D Curved Spacetimes


This page hosts the guide to the portion of my Mathematica based package TensoriaCalc which implements the 4D curved spacetime nonlinear partial differential equations of ideal magnetohydrodynamics (iMHD).

Please do feel free to use and/or modify this code, but only for the purposes of scientific research. If you do so, I merely ask that you: (I) cite the URL of this webpage in your publication(s); (II) cite this paper, during the course of which MHDSystem was developed; and (III) drop me a note. Definitely write to me if you find any bugs! Of course, questions, comments, suggestions, etc., are most welcomed too.

Updates and bugs fix history can be found within the TensoriaCalc.nb notebook, which can be downloaded below. Note that I wrote TensoriaCalc in Mathematica 8/9/10, and have tested it on my Windows 7 machine.

MHD Code
  • TensoriaCalc     First download the primary TensoriaCalc .nb file below. Open it in Mathematica and Save the file. This will create a TensoriaCalc.m file which can be loaded directly from any Mathematica session. Then download the Guide from the left column if you use the "mostly plus" metric sign covention, or from the right column if you employ the "mostly minus" one.
  • TensoriaCalc.nb
`Mostly plus' metric sign convention
Guide to  MHDSystem
`Mostly minus' metric sign convention
Guide to  MHDSystem


The MHD-related part of TensoriaCalc was developed as part of research I undertook in collaboration with Vitaly Vanchurin, at the University of Minnesota Duluth.

Future developments

I have plans to maintain this code -- and quite possibly improve upon it -- as long as I am an active researcher.