Linked Questions

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=...
3
votes
2answers
167 views

Prevent Suppression of Superscript 1 in Print [closed]

I'm trying to print Christoffel symbols of the second kind for a surface in $\mathbb R^3$. I currently am using something along the lines of ...
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?
4
votes
1answer
343 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^...
3
votes
1answer
306 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 ...
2
votes
1answer
111 views

How to identify specific Christoffel symbols and Riemann Tensor components from a general solution [closed]

I want to learn how to identify specific Christoffel Symbols and Riemman Tensor components from the general solution provided by Mathematica. Let us work out an example to see what I mean clearly. ...
1
vote
1answer
288 views

Confluent Heun function

Does the confluent Heun function exist in Mathematica? I try to evaluate the following, ...
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,...
0
votes
1answer
762 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 ...
4
votes
0answers
304 views

Linearised Einstein equations

I need to compute the linearised Einstein Equations around a fixed metric $$g_{μν}=\text{Minkowski metric} + h_{μν}$$ which is not the flat metric. Does anyone know a Mathematica package or a ...
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 ...
1
vote
0answers
564 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
604 views

Ricci tensor with Mathematica [closed]

I'm trying for first time to write a Ricci tensor with Mathematica. The code I've written is this: ...
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_{...
0
votes
0answers
38 views

How to define the covariant derivative of third order tensor in Mathematica? Such as perturbed christoffel symbols

In my work, I should calculated the perturbed Ricci tensor. The expression of perturbed ricci is: , where , and the is the covariant derivative. My question is: Is the a tensor? So that I can ...

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