Download alGR (.nb) (150 downloads)


alGR is a general relativity package written in Mathematica. The code is brief so you can easily understand and modify it. Just input your metric and the package will calculate what you need. I have employed a convenient and powerful formalism for index notation. Common tensors are represented by Mathematica functions and positive indices are lower (covariant) indices and negative indices are upper (contravariant) indices. For example, \Gamma^{1\ }_{\ 2}_{3}, is represented by Γ[-1, 2, 3]. What if you have a tensor as list and you want to do raise or lower its indices? That is supported too. Just pay attention when you should be using a function representation or a list representation of a tensor. For most users, everything is already coded so you don’t have to worry about coding.


  • A brief documentation
  • Tensor inner product of all ranks and dimensions
  • Raising and lowering indices of all ranks and dimensions
  • Connection Parameters
  • Connection Parameters
  • Riemann curvature tensor
  • Covariant derivative