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

I) The Problem There's a particular metric $,$ 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 ...
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### 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. ...
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### Confluent Heun function

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