Linked Questions

4
votes
1answer
326 views

Computing Christoffel symbols of the second kind [duplicate]

I want to compute the Christoffel-symbol for a given metric. I am using the code here, but I am missing something. The Chrisfoffel-symbol formula is $\Gamma^{\mu}_{\phantom{\mu}\nu\sigma}=\frac{1}{2}g^...
1
vote
0answers
562 views

Calculating Christoffel Symbols [duplicate]

I am totally new in the astrophysics field and I need to calculate Christoffel symbols for a model. The line element for the FLRW metric and the geodesic equation is given below: ...
1
vote
0answers
48 views

How do I define a tensor from another tensor with summations? [duplicate]

Let's say we have a rank 2 tensor $g_{ij}$. This is basically a list with a Depth of 2. Now I'd like to calculate another tensor $\Gamma_{ij}=\frac{1}{2}g^{ks}g_{...
39
votes
3answers
13k views

Differential geometry add-ons for Mathematica

I need a differential geometry tool for Mathematica. Is there any add-on? Unfortunately, Mathematica does not include such functionality or I can not find it.
12
votes
3answers
4k views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
18
votes
2answers
9k views

Using Mathematica for tensor analysis

Has anybody used tensors in Mathematica? How to properly work with them? I find Mathematica not very friendly in this field, as I am defining my own functions for lowering & raising indices, ...
8
votes
2answers
1k views

The time-like geodesics (orbits) in the Schwarzschild spacetime

I am trying to plot Schwarzschild's orbit without invoking the geodesic equation. As a reference I am using Chandrasekhar's Book (The Mathematical theory of Black Holes, Oxford University Press). In ...
7
votes
2answers
5k views

Contracting with Levi-Civita (totally antisymmetric) tensor

I have an array $v_{ijk}$ which is effectively a rank-$3$ tensor with dimensions $3\times3\times3$, and I need to contract it with $e^{ijk}$, i.e. evaluate $v_{ijk} e^{ijk}$ (see Einstein convention)....
7
votes
2answers
3k views

Compute covariant derivative in Mathematica

I need to compute covariant derivatives in Mathematica. Searching online I just found the package "Ricci" which only does symbolic computations: I instead need to do actual computations. This is ...
3
votes
2answers
3k views

How to solve a "tensor equation"?

I am trying to solve equations which looks like this: $$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$ where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example $a_1=...
5
votes
1answer
2k views

Linearized Einstein Equations with Mathematica

I need to compute the linearised Einstein Equations around a fixed metric $g_{\mu \nu}$ which is not the flat metric. Someone knows any Mathematica package or a review that can help me?
1
vote
1answer
1k views

Package for symbolic computation of christoffel symbols and parallel transports in Riemannian geometry, given the metric

I've no knowledge in mathematica (but I do in matlab), but I'd really appreciate if someone could mention what is/are the best and easy to learn mathematica package(s) for symbolic and numerical (both,...
3
votes
0answers
2k views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
3
votes
1answer
283 views

Difficulties on Mathematica code to solve Christoffel Symbols of a particular metric

I) The Problem There's a particular metric $[1],[2]$ in general relativity which is written as: $$ds^{2} = -[c^2-v_{s}^2f(r_{s})^2]dt^2+v_{s}f(r_{s})dtdx+v_{s}f(r_{s})dxdt+ dy^2+dz^2 \tag{1}$$ So ...
0
votes
1answer
758 views

Scalar from tensor contraction

I'm trying to calculate the Kretschmann scalar in mathematica, it is given by: $c = R^{abcd} R_{abcd}$ Where $R^{abcd}$ is the Riemann tensor. I'm following this MSE post so I modified it to get ...

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