Linked Questions

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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 ...
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. ...
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
307 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 ...
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 ...
1
vote
1answer
289 views

Confluent Heun function

Does the confluent Heun function exist in Mathematica? I try to evaluate the following, ...
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: ...
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 ...
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 ...
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
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,...
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 ...
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 ...
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)....
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_{...

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