# Questions tagged [xact]

Questions about xAct, a suite of packages for tensor computer algebra, which includes the packages xCore, xPerm, xTensor, and xCoba.

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### Compute curvature tensor constructed by a shifted connection

I'm using xAct package to compute the curvature tensor from a specific connection, of the form $\Gamma^a_{bc}= \mathring{\Gamma}^a_{bc} + S^a_{\:bc}$, where the first term is the Levi Civita ...
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### (xAct) AllContractions with sum of terms

I'm doing some GR calculations using xAct package. In order to find all dimensional-dependent-identities (DDIs), mathematica has to apply the ...
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### Difference between variables and expressions for ReplaceAll

I'm doing some GR calculations with xAct. I get an expression that is heavy. In order to simplify the results, I try to use the function ReplaceAll in simple cases. ...
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### How to effectively substitute variables in xAct?

I am trying to find the gauge field equation by varying the Born-Infeld Action with the help of xact package. I use the following ...
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### Varying Einstein-Hilbert action through xAct gives extra terms

I am trying to find the associated field equation by varying this action: $$S=\int d^4x \sqrt{-g}(\kappa \mathcal{R}+\Lambda)$$ This should give me the below field equation when I vary above w.r.t the ...
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### How to convert xAct output to FeynCalc input?

For the packages xAct and Feyncalc, is there a way to convert xAct output into Feyncalc input? I have an expression of one rank and four rank tensors as an output from xAct. The number of terms is ...
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### Metric pertubation in xAct

I start to learn xAct. Following this thread: expanding-the-riemann-tensor-perturbation I noticed that xAct set a default perturbation to the metric by: ...
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1 vote
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### Feynman amplitude calculation for a Feynman diagram of gravitons in xAct

Any tutorial example how to calculate Feynman rules from a Lagrangian of gravitons in xAct and how to implement it for calculating its Feynman amplitude for a given diagram involving gravitons in xAct?...
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### How can I define a d-dimensional metric on mathematica with abstract components?

I want to define on Mathematica the (d+1)-dimensional metric: $ds^2 =G_{\mu\nu}dx^{\mu}dx^{\nu}= 2tdt^2 + g_{ij}(t,x)dx^idx^j$ where latin indices go $i,j=1,...,d-1$ and $g_{ij}$ are unknown ...
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### How to define a Kerr-Schild metric in xAct?

A Kerr-Schild can be expressed as $g_{ab}=\eta_{ab}+\phi k_a k_b$, where $\eta_{ab}$ is Minkowski metric, $\phi$ is a scalar function and $k_a$ is a (co)vector field which is null and geodetic with ...
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1 vote
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### Finding Petrov type of a metric

Is there a subpackage in xAct (or another Mathematica package for general relativity calculations) to determine the Petrov type of a metric? I understand that xAct has a lot of subpackages for ...
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### How to write the metric tensor in n-dimensions using xAct?

I am trying to reproduce some calculations from a paper, where they express the angular part of the metric as a solid angle in (d-2) dimensions: where I know how to calculate the metric tensor using ...
1 vote
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### Help with gravitational waves plot/animation with Schwarzschild metric using xAct package and ListPlot3D

Update: I have now successfully derived the gravitational wave equation. I used this template with slight modifications. The screenshot of success is shown below, followed by the code. Now I need help ...
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### Using xTensor and XCoba together

Im trying to use both packages together in order to study the Bondi-Sachs metric. I'm having some trouble making it work. I have my main manifold $M$, and a "sub-manifold" $S$ which is the ...
1 vote
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### Scalar field theory in xAct mathematica

I have this action I want to vary this action. How do I do it? This is my code ...
1 vote
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### How to make the Levi-Civita express the value from the package xAct?

I try to use the package xAct to compute the 1-form field from 3-form field as shown in the picture below. However, the value of Levi-Civita or epsilong does not express. How could I solve this? ...
1 vote
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### What is the right way to simplify a tensor expression (with many indices, but no derivatives) in Mathematica?

After not finding the desired capabilities in base Mathematica, I am trying to use xAct`xTensor package. It appears that I do not need most of it capabilities ...
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### Why are Christoffels vanishing depending on choice of basis (xAct)?

Hi all (probably Jose), I am not sure if I am misunderstanding some fundamental GR topic or if I am using the package wrong. I would at some point like to contract over the components of the metric ...
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### Is there a builtin function to expand covariant derivatives in terms of the metric (xAct, xCoba)

Firstly, I realize that this is somewhat easy to do with replacement rules as a one off. However, I see that in my work this is something that I may like to use occasionally without much effort. What ...
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### Calculating Eigenvalues using xAct

I'm trying to calculate the eigenvalues of the following system which originates from here (Appendix B): \begin{align} i{\xi}_{0}\hat{\tilde{\gamma}}_{ij} &= 2i\tilde{\gamma}_{k(i}\xi_{j)}\...
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### Solving equations of motion in xAct

Varying with respect to metric (https://github.com/xAct-contrib/examples/blob/master/ActionVariation_Metric_Fields.nb) I obtained equations of motion for Einstein Gauss Bonnet gravity with two scalar ...
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### How would I go about defining a metric with undetermined functions and then set certain components of the Ricci Tensor zero and solve the PDE(s)?

I am a new user and have so far figured out how to calculate quantities with explicitly defined metrics (schwarzschild, kerr etc.) What I want to ultimately do is define a generic metric with ...
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### Define Conformal Metric in xAct

For my thesis, I'm reproducing the results of a paper here by Alic et al in Mathematica using the package xAct. I'm able to reproduce the standard $3+1$ ...
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### Tensor equation problem (xact package)

So i want to solve the tensor equation P1[-μ,-ν]=0 with respect to A[r] and then B[r] but the problem is when hitting shift-enter the tensor given is way too long (if i press "show all" my ...
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1 vote
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### Define a normalized vector field with xTensor

I just started to learn how to use xAct and xTensor. I would like to define the following vector field on a manifold equipped with a Lorentzian metric. My attempt was ...
1 vote
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### How to define a traceless tensor with xAct

I would like to define a tensor $A_i^j$ which is traceless ($A_i^i = 0$) and to obtain $A_i^j \delta^i_j = 0$ with xAct / xTensor / xCoba. I first tried defining an antisymmetric tensor, since they ...
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### How to omit (not to display) the function arguments using TexAct package?

I try to use TexPrint command in the TexAct package, and the expression contains Derivative[1][f][r[]], H2[t[], r[]]etc., is it possible to avoid displaying these ...
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### xAct : how to define f to be a function of two variables?

f is a function of the coordinates x and y, how can I use the command DefScalarFunction to do this? ...
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I am trying to do perturbation, it involved terms like this: $\partial_{l}(g^{lp} g^{kq} h_{pq}) (\partial_{i}g_{jk})$ I want to obtain the simplified result of the components {i,j} all other indices ...