Questions tagged [xact]
Questions about xAct, a suite of packages for tensor computer algebra, which includes the packages xCore, xPerm, xTensor, and xCoba.
53
questions
1
vote
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
votes
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_{...
1
vote
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 ...
0
votes
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
vote
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:
<...
0
votes
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
vote
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 ...
0
votes
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
vote
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
votes
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 ...
0
votes
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
vote
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) ...
3
votes
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
vote
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
...
0
votes
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 ...
0
votes
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} + \...
1
vote
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 ...
0
votes
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
votes
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
vote
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 ...
0
votes
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 ...
0
votes
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
vote
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
votes
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
votes
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
votes
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 ...
1
vote
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
vote
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
vote
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
$$
D_a D^a \phi\, ...
2
votes
0answers
101 views
Calculation of Einstein theory: How to gauge condtion to cancel perturbation terms in xact
I try to use the xAct Mathematica package for deal with the Einstein field equation in weak field. I can get
$R=-h^{ab}_{,ab}+\frac{\eta^{ab}}{2}\left[h^c_{c,ab}-\Delta h_{ab}\right]$,
Now, I want ...
1
vote
0answers
253 views
How to apply perturbed metric in xPert calculations?
I am using xAct (xTras and xPert) for doing linear perturbations. I almost know how to constrct the perturbed equations while I dont know how to apply the perturbed metric in the final equations. I ...
2
votes
1answer
209 views
Is it possible to implement the Palatini formalism in xAct?
In the Palatini formalism, the connections $\Gamma^\alpha_{\beta\gamma}$ are considered independent variable togheter with the metric; as a consequence Ricci and Rieman tensors corresponding to the ...
1
vote
0answers
356 views
Obtaining Explicit Expressions for Tensor Contractions in xCoba
I Would like to know, how to reduce a general Tensor expression such as Cd[-c][Cd[c][h[-a,-b]]] (D'alambertian of some unknown two component tensor) to an explicit ...
0
votes
0answers
228 views
How to perform 3+1 decomposition of spacetime with xTensor?
I am new to xTensor. I would like to perform 3+1 decomposition of spacetime with xTensor, but I do not have any clue. Although in xTensorDoc.nb, the author gave some hint, I absolutely have no idea of ...
3
votes
2answers
1k views
How to install xAct in windows 10 correctly?
I just found one powerful computational tool xAct. Unfortunately, I cannot get it installed correctly. The installation instruction provided by the website is too old, and in windows 10, there is no ...
4
votes
1answer
1k views
How to define a tensor in xAct for Mathematica?
I'm working on a cosmological model for general relativity, and I need to define a tensor and assign values to this. For example, a tensor $A_{\mu\nu}$ that is function of other tensors:
$$A_{\mu\nu}...
3
votes
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
votes
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
votes
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
votes
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
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
...
