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Questions tagged [xact]

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

127 questions
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Evaluating covariant derivative terms of a scalar function (xAct, xTras)

I am trying to use xAct package to calculate certain mixing terms of $\nabla_{\chi} b$ of a scalar function $b[ \tau, r, \theta, \phi]$ for a modified metric. Here is my Code: << xAct`xTras` ddim = 4; coords = {\[Tau][], r[], \[Theta][],…
Muktadir Rahman
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4
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1 answer

xAct xCoba: Geodesic Equation in Components

I am using xAct package and I would like to get geodesic equations in components for Schwarzshild metric (for instance). DefManifold[M4, 4, {\[Alpha], \[Beta], \[Rho], \[Sigma], \[Mu], \[Nu], \[Lambda]}] DefScalarFunction /@ {f,…
Luciano Barosi
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Why will xAct/xCoba not contract these basis elements?

Consider the following minimal working example: << xAct`xTras` DefManifold[spacetime, 4, {α, β, γ, μ, κ, ν, ξ, ρ, ζ, τ}] DefMetric[{3, 1, 0}, Met[-μ, -ν], CD, {";", "∇"}, PrintAs -> "g"] (* 1 *) DefTensor[u[-μ], spacetime] DefChart[coords,…
akozi
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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 tensor which should involve expanding covariant…
akozi
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3
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1 answer

Simplifying Expressions in xAct

I am completely new to xAct and was wondering if it is possible to tell xAct how to simplify expressions. Is there, for example, a way (e.g. in form of a supplied rule) to automatically simplify Maxwell equations given as CD[-b][CD[-a][A[b]]] -…
olse barn
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3
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1 answer

xAct rule for antisymmetrization

using the xAct I'm trying to make a rule that the antisymmetrization in three indices of an expression goes to zero. Namely I have the killing vector $$ \xi^a $$ defined using DefTensor[\[xi][a],M,KillingVectorOf -> metric] with $M$ being the…
Nitaa a
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Dealing with covariant derivatives (xCoba)

I do not understand why the output of the two commands: metric[-c, -d] (CD[d][RicciScalar[CD][]]) (CD[c][RicciScalar[CD][]]) // Simplify, (CD[-c][RicciScalar[CD][]]) (CD[c][RicciScalar[CD][]]) // Simplify, is different. The first one outputs a…
Janstillerion
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How to use CTensor for the Maxwell stress tensor F?

I have used the CTensor to compute an equation of motion. Everything is ok but the stress tensor F. How can I rewrite this tensor using CTensor. The needed definitions are as follows: DefManifold[M, 6, {\[Alpha], \[Beta], \[Sigma], \[Delta],…
Perfect Fluid
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Finding specific form of an equation from the general form in xAct

I'm aware the title isn't very clear - couldn't think of a better one sorry. I think my problem is best illustrated with the simplest example I can make. Quit[] << xAct`xTensor` << xAct`ExpressionManipulation` << xAct`xCoba` Some setup to remove…
A C
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functional derivative with respect to the partial derivative of the metric with xAct

I want to compute the functional derivative with respect to a partial derivative of the metric with the mathematica package xAct. This is what I have tried so far: DefManifold[M, 4, IndexRange[a, z]] DefMetric[-1, met[-a, -b], CD, PrintAs -> "g",…
Carmen López Jurado
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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 surfaces of constant $t$ and $r$. Some tensors are defined…
Gianni Boschetti
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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 I would like in math notation is to go from the…
akozi
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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…
fasdgr
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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 variables dependence[t[], r[]] by using TexPrint or other commands? Since I want a…
Jh Wang
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in xAct, how to set the components of a tensor to be zero

OBASuppose there is a vector $A^{a}$ appears in the result in different component form like $A^{\mu},A^{\nu},A^{\alpha}...$, I want all of them to be zero because the components of the tensor are zero, what method can I use?
Jh Wang
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