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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23 views

How to define commutative covariant derivatives in xTensor

I'm new with working xAct package and got stuck defining covariant derivatives that commute with each other. I want to simulate flat space-time. And here is my code ...
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0answers
34 views

How to expand the basis in a tensorial expression?

I have a very complicated expression (that cannot be written here). In fact, it is a tensorial equation (an equation of motion) where the first component of it is needed (the tt component). After ...
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0answers
34 views

How to compute gauge variation of expression?

Suppose I have a symmetric tensor field $h_{\mu\nu}$ I want to implement somehow the following gauge variation of this tensor field as follows $\delta h_{\mu\nu} = \nabla_{\mu}\epsilon_{\nu} + \...
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0answers
65 views

How can I devote all the cores to Mathematica?

I have a problem with the calculations speeds in xAct package. In fact, some of them take lots of seconds. Is there any way to speed up the calculations by engaging all the cores for Mathematica (or ...
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0answers
32 views

How to collect a tensor in an equation?

Is there any way to collect a special tensor (for example the metric tensor) in a tensorial equation? I mean a command like Collect in the non-tensorial ...
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1answer
60 views

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 ...
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1answer
54 views

Increasing the time constraint on EulerEquations [closed]

How can I set the Infinity time constraint in EulerEquations? Actually, there is an error I don't have any idea about. Can you ...
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0answers
50 views

Specification the metric in xact [duplicate]

How can I find the unknown function V(r) by specifying the metric met in this gravitational theory? I have defined the manifold ...
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0answers
86 views

How can I define another metric (disformal transformation) in xAct?

I'm using the xAct package. I want to define two metrics with the disformal transformation relation $\qquad \bar{g}_{\mu\nu}=A(\phi) g_{\mu\nu}+B(\phi)\nabla_\mu \phi\nabla_\mu \phi ,$ where $g_{\...
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0answers
66 views

Evaluating covariant derivative for perturbed metric given background metric

I want to use Mathematica to evaluate an expression like; $h^{\alpha\beta}_{\,\,\,\,\,|\mu}h_{\alpha\beta\,|\nu} +\mbox{similar}$ where $h_{\alpha\beta}$ is the perturbation to a specified metric (...
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1answer
56 views

Having problem with ChangeOfCurvature function in xAct

I'm working on a metric-affine theory where the affine connection is independent of the metric. I've solved the general connection in terms of Levi-Civita connection of the metric plus a vector field ...
2
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1answer
136 views

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). ...
2
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1answer
103 views

How to apply Partial differentiation w.r.t. tensors?

Let's say I have an expression like $\,a^{I}=2b^{I}+3c^{I}$ where $I$ stands for an arbitrarily large set of indices. It's known that $\,\frac{\partial a^K}{\partial c^{L}}=3\,\delta^K_L$ (equals a ...
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3answers
196 views

Simplify Kronecker Delta expression

How to obtain Kronecker delta summation rule using Wolfram Mathematica: $$ \delta_{ij}\delta_{jk}=\delta_{ik} $$ The following code does not produce the result. ...
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3answers
115 views

How to use “Cases” for isolating terms of a sum in a nice way?

I'd like to isolate some terms with specific patterns within a sum that I called chunk. ...
4
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1answer
93 views

Manipulations with tensors that keep so(3,1) symmetry manifest

I am doing some manipulations with tensors in curved background. There are, however, coordinates, where Lorentz symmetry is manifest. So, on one hand, I am dealing with particular coordinates and, on ...
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0answers
126 views

Cosmological perturbation using xPand - metric's signature error

I need to construct the Ricci Tensor, $R_{\mu \nu}$, using the following metric: $ds^{2}=-N^{2}dt^{2}+a^{2}(t)dx^{i}dx^{i}$ and I need to perturbe it using the following pertubed metric: $ds^{2} = -...
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0answers
49 views

How can I put the gradient of a scalar field in xAct? [closed]

[ for example the gradient of scalar field to square in the Gauss-Bonnet action?
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0answers
87 views

How to define a constraint implying covariant derivatives in XTensor/XAct?

I have two manifolds: M and M1 with metrics g and g1. ...
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1answer
77 views

How to change the dimension of a tensor inside a loop using XAct/XTensor?

I'd like to define a function CDOrder[k] to compute the k-th order covariant derivative of a vector ...
2
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1answer
257 views

Unable to simplify tensor expressions with xAct

Using xAct package in Mathematica, I am trying to obtain expansions of Ricci scalar upto second order in metric perturbations. Although I am able to obtain the perturbed expressions, Mathematica/xAct ...
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0answers
209 views

Solving Relaxed Einstein Equation with xAct and xTensor packages

First time question, involving tensor calculus. I am entirely new to Mathematica and don't understand most of its conventions or jargon. I'm trying to do tensor calculations in GR. I've ...
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1answer
376 views

Define tensor made of other tensors in xAct

I'm fairly new to the xAct project for Mathematica, but feel like I understand fairly well how to define an arbitrary tensor using xTensor. My problem is that I want to define a tensor that is ...
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0answers
57 views

Substitute function of derivatives and its argument in xAct

I am using xAct to do some tensor computation. Consider the following term CD[-a][CD[a][\[Phi][]]]CD[-b][CD[b][\[Phi][]]] which is latex is $$ D_a D^a \phi\, ...
2
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0answers
80 views

Calculation of Einstein theory: How to gauge condtion to cancel perturbation terms in xact

I try to use the xAct Mathematica package for deal with the Einstein field equation in weak field. I can get $R=-h^{ab}_{,ab}+\frac{\eta^{ab}}{2}\left[h^c_{c,ab}-\Delta h_{ab}\right]$, Now, I want ...
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0answers
215 views

How to apply perturbed metric in xPert calculations?

I am using xAct (xTras and xPert) for doing linear perturbations. I almost know how to constrct the perturbed equations while I dont know how to apply the perturbed metric in the final equations. I ...
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1answer
187 views

Is it possible to implement the Palatini formalism in xAct?

In the Palatini formalism, the connections $\Gamma^\alpha_{\beta\gamma}$ are considered independent variable togheter with the metric; as a consequence Ricci and Rieman tensors corresponding to the ...
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0answers
289 views

Obtaining Explicit Expressions for Tensor Contractions in xCoba

I Would like to know, how to reduce a general Tensor expression such as Cd[-c][Cd[c][h[-a,-b]]] (D'alambertian of some unknown two component tensor) to an explicit ...
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0answers
191 views

How to perform 3+1 decomposition of spacetime with xTensor?

I am new to xTensor. I would like to perform 3+1 decomposition of spacetime with xTensor, but I do not have any clue. Although in xTensorDoc.nb, the author gave some hint, I absolutely have no idea of ...
3
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2answers
856 views

How to install xAct in windows 10 correctly?

I just found one powerful computational tool xAct. Unfortunately, I cannot get it installed correctly. The installation instruction provided by the website is too old, and in windows 10, there is no ...
4
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1answer
974 views

How to define a tensor in xAct for Mathematica?

I'm working on a cosmological model for general relativity, and I need to define a tensor and assign values to this. For example, a tensor $A_{\mu\nu}$ that is function of other tensors: $$A_{\mu\nu}...
3
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0answers
131 views

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. ...
1
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1answer
108 views

Output format not right in xAct

I started using xAct to perform some computations. I copied the xAct folder in the /.Mathematica/Applications folder in my Ubuntu system. I loaded it and created the manifold and defined the metric. ...
6
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0answers
242 views

Variating the derivative of the metric using xTensor

I would like Mathematica to be able to use the following expression in a more complicated computation: \begin{equation} \tag{1}\frac{\delta{}g^{\alpha\beta}_{\;{},\gamma}\left(x\right)}{\delta{}g^{\mu\...
3
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1answer
285 views

Calculating e.g. Euler density or Riemann tensor's square for a given metric using xAct package

I have started to learn about the xAct package to do some general relativistic calculations and whereas there might be other codes available, I would like to get my answer in terms of this package's ...
5
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1answer
380 views

Copy xAct expression to LaTeX

How can I copy an xAct expression to LaTex? Using the usual command TeXForm[] gives the xAct structure, I would like to get the printed form. For example $$ \text{TeXForm}[\nabla_a\phi\nabla^a\phi] $$...
3
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1answer
911 views

Expanding the Riemann tensor (perturbation)

I am trying to expand the following term (via the perturbation expansion $g_{\mu\nu} = \eta_{\mu\nu} + \kappa h_{\mu\nu}$): $$ \frac12 \epsilon^{abcd}R^e_{fcd}R^f_{eab} $$ Where $R$ is the Riemann ...
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2answers
2k views

How can I define a metric in xAct?

I'm using "xAct" package and I want to define a my metric, that is a non standard metric. For example, my metric is diagonal ...
9
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2answers
3k views

Perturbation theory in general relativity using xAct

I'm trying to use the xAct Mathematica package for manipulating tensors, and I'd like to plug in a metric into the perturbation equations to first order in general relativity, and have everything ...
33
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1answer
1k views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
4
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0answers
555 views

Tensor product involving Levi Civita symbol

I'm working with xAct package. I've defined the tensor component values and my issue is that I want an expression involving Levi Civita symbols and tensor components, I don't know how to deal with it. ...