Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [xact]

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

1
vote
0answers
24 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
votes
1answer
40 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
votes
1answer
86 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
votes
1answer
61 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 ...
1
vote
3answers
136 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
votes
3answers
102 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
votes
1answer
77 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 ...
0
votes
0answers
97 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} = -...
1
vote
0answers
42 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
votes
0answers
75 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
votes
1answer
68 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
votes
1answer
181 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 ...
1
vote
0answers
153 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
vote
1answer
268 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
vote
0answers
47 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
votes
0answers
72 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
vote
0answers
182 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
157 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
vote
0answers
263 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
votes
0answers
175 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
votes
1answer
643 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
votes
1answer
841 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
votes
0answers
118 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
vote
1answer
85 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
votes
0answers
224 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
votes
1answer
250 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
333 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
votes
1answer
830 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 ...
2
votes
2answers
1k 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
votes
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
votes
1answer
994 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
votes
0answers
456 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. ...