Questions tagged [xact]
Questions about xAct, a suite of packages for tensor computer algebra, which includes the packages xCore, xPerm, xTensor, and xCoba.
41
questions
1
vote
1answer
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
...
0
votes
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 ...
0
votes
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} + \...
1
vote
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 ...
0
votes
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 ...
3
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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_{\...
1
vote
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 (...
2
votes
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
votes
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
votes
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 ...
1
vote
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.
...
3
votes
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
votes
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 ...
0
votes
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} = -...
1
vote
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?
2
votes
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.
...
2
votes
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
votes
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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
$$
D_a D^a \phi\, ...
2
votes
0answers
80 views
Calculation of Einstein theory: How to gauge condtion to cancel perturbation terms in xact
I try to use the xAct Mathematica package for deal with the Einstein field equation in weak field. I can get
$R=-h^{ab}_{,ab}+\frac{\eta^{ab}}{2}\left[h^c_{c,ab}-\Delta h_{ab}\right]$,
Now, I want ...
1
vote
0answers
215 views
How to apply perturbed metric in xPert calculations?
I am using xAct (xTras and xPert) for doing linear perturbations. I almost know how to constrct the perturbed equations while I dont know how to apply the perturbed metric in the final equations. I ...
2
votes
1answer
187 views
Is it possible to implement the Palatini formalism in xAct?
In the Palatini formalism, the connections $\Gamma^\alpha_{\beta\gamma}$ are considered independent variable togheter with the metric; as a consequence Ricci and Rieman tensors corresponding to the ...
1
vote
0answers
289 views
Obtaining Explicit Expressions for Tensor Contractions in xCoba
I Would like to know, how to reduce a general Tensor expression such as Cd[-c][Cd[c][h[-a,-b]]] (D'alambertian of some unknown two component tensor) to an explicit ...
0
votes
0answers
191 views
How to perform 3+1 decomposition of spacetime with xTensor?
I am new to xTensor. I would like to perform 3+1 decomposition of spacetime with xTensor, but I do not have any clue. Although in xTensorDoc.nb, the author gave some hint, I absolutely have no idea of ...
3
votes
2answers
856 views
How to install xAct in windows 10 correctly?
I just found one powerful computational tool xAct. Unfortunately, I cannot get it installed correctly. The installation instruction provided by the website is too old, and in windows 10, there is no ...
4
votes
1answer
974 views
How to define a tensor in xAct for Mathematica?
I'm working on a cosmological model for general relativity, and I need to define a tensor and assign values to this. For example, a tensor $A_{\mu\nu}$ that is function of other tensors:
$$A_{\mu\nu}...
3
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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 ...
2
votes
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
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
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
votes
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. ...
