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. ...
