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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1answer
31 views

Is it possible to defining a scalar with CTensor?

I have a tensor (rank zero) or a scalar $\phi$ which defined as DefTensor[\[Phi][], M] on manifold $M$. After defining the metric, how can I use ...
2
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1answer
34 views

How to compute functional derivative against vector in xAct, xTensor or xTras?

I want to compute the functional derivative against vectors. For example, I have an object that looks like this $R = h_{ijkl}a^i a^j a^k a^l$ I need to compute $\frac{\delta R}{\delta a^p}= 4 h_{...
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0answers
36 views

Kretschmann scalar in xTensor and xCoba

How do I calculate the Kretschmann scalar $K=R_{abcd}R^{abcd}$ with xTensor and xCoba? I have found the functions Kretschmann and ...
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0answers
41 views

Rewriting all terms in terms of Riemann tensor

Is there any command to rewrite all the curvature terms like $R$ or $R_{\alpha\beta}$ or $R_{\alpha\beta}^{~~~~~\gamma\delta}$ in terms of the Riemann tensor $R_{\alpha\beta\gamma\delta}$ and the ...
1
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1answer
43 views

How to work with Levi civita tensor in xAxt?

Is there any command to work with the Levici vita tensor? In fact, I found LeviCivitaTensor, however, in calculations it doesn't seem practical. see the example: <...
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0answers
19 views

xAct: partition set of indices

In my example the manifold M is a Lie group G, say generated by generators {T_A} of the corresponding algebra and I would like to be able to expand the Lie group G into those of a subgroup H, say {T_a}...
1
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0answers
23 views

Derivatives with dummy indices not commutative after 3d derivative?

Recently I've encountered the following issue in xAct. I've defined the Manifold and tensors in the following manner Then consider the following expressions. In the case where there are 2 ...
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0answers
19 views

Hamiltonian Analysis in xAct: Variation wrt time derivative of fields

I'd like to use the xAct package to perform the Hamiltonian analysis of a complicated action. To that end, it would be useful to introduce a chart and split indices into "temporal" and "spatial" parts....
1
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0answers
20 views

How to combine symmetrized tensor expressions into single expression in xAct

Let's sayI have the following expression in xAct where covariant derivatives are commutative, $\epsilon$ and $h$ are symmetric tensors. As we can see this expression is equivalent to If we ...
2
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0answers
71 views

How to remove the Riemann tensor derivatives using Bianchi identity?

For the third-order Lovelock gravity, after varying the Lagrangian versus the metric, I found some derivatives of the Riemann tensor which should not be appeared. How can I remove them? Maybe using ...
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0answers
43 views

How to get rid of these matrices?

I have divided a complicated Lagrangian to some separated terms to be able to Simplify it. The thing is, in the general case (non-divided Lagrangian) the problem is ...
1
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2answers
47 views

How to set up symplectic geometry without(!) metric (with xAct/xTensor)?

I want to define a symplectic manifold with symplectic form $\Omega_{[ab]}$ with $\Omega_{ab}\Omega^{ac} = \delta^c_b$, but without having a metric. I define a manifold and an antisymmetric (2,0) ...
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0answers
44 views

How to speed up xTensor simplification?

I need to compute a variation of the 4th rang symmetric tensor. I've written a code that successfully computes it, but when I use the resulting tensor to compute the second variation the ...
1
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1answer
74 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
40 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
43 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
73 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
39 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 ...
3
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1answer
112 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 ...
1
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1answer
116 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
52 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
143 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_{\...
1
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0answers
108 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 (...
2
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1answer
74 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
258 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
158 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
309 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. ...
3
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3answers
124 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
107 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 ...
1
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0answers
54 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?
2
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0answers
103 views

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

I have two manifolds: M and M1 with metrics g and g1. ...
2
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1answer
97 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
354 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 ...
2
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0answers
308 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 ...
1
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1answer
493 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 ...
1
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0answers
78 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
101 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 ...
1
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0answers
253 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 ...
2
votes
1answer
209 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 ...
1
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0answers
356 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 ...
0
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0answers
228 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
1k 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
1k 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
146 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. ...
2
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1answer
138 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 ...
6
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0answers
266 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\...
5
votes
1answer
345 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
votes
1answer
433 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
1k 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 ...
3
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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 ...