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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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Compute curvature tensor constructed by a shifted connection

I'm using xAct package to compute the curvature tensor from a specific connection, of the form $\Gamma^a_{bc}= \mathring{\Gamma}^a_{bc} + S^a_{\:bc}$, where the first term is the Levi Civita ...
ayberk çakmak's user avatar
0 votes
0 answers
44 views

(xAct) AllContractions with sum of terms

I'm doing some GR calculations using xAct package. In order to find all dimensional-dependent-identities (DDIs), mathematica has to apply the ...
TrodaroX's user avatar
2 votes
2 answers
55 views

Difference between variables and expressions for ReplaceAll

I'm doing some GR calculations with xAct. I get an expression that is heavy. In order to simplify the results, I try to use the function ReplaceAll in simple cases. ...
TrodaroX's user avatar
2 votes
0 answers
78 views

How to effectively substitute variables in xAct?

I am trying to find the gauge field equation by varying the Born-Infeld Action with the help of xact package. I use the following ...
codebpr's user avatar
  • 2,263
3 votes
1 answer
111 views

Varying Einstein-Hilbert action through xAct gives extra terms

I am trying to find the associated field equation by varying this action: $$S=\int d^4x \sqrt{-g}(\kappa \mathcal{R}+\Lambda)$$ This should give me the below field equation when I vary above w.r.t the ...
codebpr's user avatar
  • 2,263
2 votes
0 answers
61 views

Defining a tensor in terms of its trace and other tensors

I'm starting to learn xAct for tensor operations. So I am dealing with 3 tensors: $T_{abc}$, $Q_{abc}$ and a metric tensor $g_{ab}$; with these tensors I have an equation like $$T_{abc} = Q_{abc} + ...
ayberk çakmak's user avatar
3 votes
0 answers
68 views

Why will xAct/xCoba not contract these basis elements?

Consider the following minimal working example: ...
akozi's user avatar
  • 873
1 vote
0 answers
30 views

Tensors without explicit specifications in xCoba

In the standard Schwarzschild setup I have the following tensor: ...
mster8390's user avatar
2 votes
1 answer
135 views

Using Reduce to simplify (not solve) system of equations

I'm dealing with a Mathematica program that generates a set of coupled non-linear equations involving an unknown function and its derivatives with respect to at least one independent variable. My goal ...
José Ferreira's user avatar
2 votes
0 answers
63 views

functional derivative with respect to the partial derivative of the metric with xAct

I want to compute the functional derivative with respect to a partial derivative of the metric with the mathematica package xAct. This is what I have tried so far: ...
Carmen López Jurado's user avatar
3 votes
1 answer
108 views

xAct/xCoba and DSolve Don't Work Together

Context I'm trying to derive the Reissner-Nordstrom metric for a charged nonrotating black hole using xAct. The idea is to first have a metric of form $$ds^2 = e^{2\alpha(r)}dt^2-e^{2\beta(r)}dr^2-r^...
mijucik's user avatar
  • 157
0 votes
0 answers
50 views

How to convert xAct output to FeynCalc input?

For the packages xAct and Feyncalc, is there a way to convert xAct output into Feyncalc input? I have an expression of one rank and four rank tensors as an output from xAct. The number of terms is ...
NovoGrav's user avatar
0 votes
0 answers
117 views

Metric pertubation in xAct

I start to learn xAct. Following this thread: expanding-the-riemann-tensor-perturbation I noticed that xAct set a default perturbation to the metric by: ...
Dr. phy's user avatar
  • 287
1 vote
0 answers
73 views

Feynman amplitude calculation for a Feynman diagram of gravitons in xAct

Any tutorial example how to calculate Feynman rules from a Lagrangian of gravitons in xAct and how to implement it for calculating its Feynman amplitude for a given diagram involving gravitons in xAct?...
NovoGrav's user avatar
2 votes
0 answers
106 views

How can I define a d-dimensional metric on mathematica with abstract components?

I want to define on Mathematica the (d+1)-dimensional metric: $ ds^2 =G_{\mu\nu}dx^{\mu}dx^{\nu}= 2tdt^2 + g_{ij}(t,x)dx^idx^j $ where latin indices go $i,j=1,...,d-1$ and $g_{ij}$ are unknown ...
Mike Ehrmantraut's user avatar
2 votes
0 answers
149 views

How to define a Kerr-Schild metric in xAct?

A Kerr-Schild can be expressed as $g_{ab}=\eta_{ab}+\phi k_a k_b$, where $\eta_{ab}$ is Minkowski metric, $\phi$ is a scalar function and $k_a$ is a (co)vector field which is null and geodetic with ...
Dongba's user avatar
  • 21
1 vote
0 answers
78 views

Finding Petrov type of a metric

Is there a subpackage in xAct (or another Mathematica package for general relativity calculations) to determine the Petrov type of a metric? I understand that xAct has a lot of subpackages for ...
jay121's user avatar
  • 43
0 votes
0 answers
162 views

How to write the metric tensor in n-dimensions using xAct?

I am trying to reproduce some calculations from a paper, where they express the angular part of the metric as a solid angle in (d-2) dimensions: where I know how to calculate the metric tensor using ...
Matheus Macêdo's user avatar
1 vote
0 answers
140 views

Help with gravitational waves plot/animation with Schwarzschild metric using xAct package and ListPlot3D

Update: I have now successfully derived the gravitational wave equation. I used this template with slight modifications. The screenshot of success is shown below, followed by the code. Now I need help ...
kevin Tah N.'s user avatar
2 votes
0 answers
171 views

Using xTensor and XCoba together

Im trying to use both packages together in order to study the Bondi-Sachs metric. I'm having some trouble making it work. I have my main manifold $M$, and a "sub-manifold" $S$ which is the ...
Gianni Boschetti's user avatar
1 vote
0 answers
225 views

Scalar field theory in xAct mathematica

I have this action I want to vary this action. How do I do it? This is my code ...
Apurv Keer's user avatar
1 vote
0 answers
86 views

How to make the Levi-Civita express the value from the package xAct?

I try to use the package xAct to compute the 1-form field from 3-form field as shown in the picture below. However, the value of Levi-Civita or epsilong does not express. How could I solve this? ...
TaKol Tang's user avatar
1 vote
1 answer
98 views

What is the right way to simplify a tensor expression (with many indices, but no derivatives) in Mathematica?

After not finding the desired capabilities in base Mathematica, I am trying to use xAct`xTensor package. It appears that I do not need most of it capabilities ...
fiktor's user avatar
  • 166
3 votes
1 answer
101 views

Why are Christoffels vanishing depending on choice of basis (xAct)?

Hi all (probably Jose), I am not sure if I am misunderstanding some fundamental GR topic or if I am using the package wrong. I would at some point like to contract over the components of the metric ...
akozi's user avatar
  • 873
2 votes
1 answer
253 views

Is there a builtin function to expand covariant derivatives in terms of the metric (xAct, xCoba)

Firstly, I realize that this is somewhat easy to do with replacement rules as a one off. However, I see that in my work this is something that I may like to use occasionally without much effort. What ...
akozi's user avatar
  • 873
0 votes
0 answers
78 views

Calculating Eigenvalues using xAct

I'm trying to calculate the eigenvalues of the following system which originates from here (Appendix B): \begin{align} i{\xi}_{0}\hat{\tilde{\gamma}}_{ij} &= 2i\tilde{\gamma}_{k(i}\xi_{j)}\...
Kabouter9's user avatar
  • 163
2 votes
0 answers
347 views

Solving equations of motion in xAct

Varying with respect to metric (https://github.com/xAct-contrib/examples/blob/master/ActionVariation_Metric_Fields.nb) I obtained equations of motion for Einstein Gauss Bonnet gravity with two scalar ...
fasdgr's user avatar
  • 407
0 votes
0 answers
68 views

How would I go about defining a metric with undetermined functions and then set certain components of the Ricci Tensor zero and solve the PDE(s)?

I am a new user and have so far figured out how to calculate quantities with explicitly defined metrics (schwarzschild, kerr etc.) What I want to ultimately do is define a generic metric with ...
jay121's user avatar
  • 43
2 votes
1 answer
318 views

Define Conformal Metric in xAct

For my thesis, I'm reproducing the results of a paper here by Alic et al in Mathematica using the package xAct. I'm able to reproduce the standard $3+1$ ...
Kabouter9's user avatar
  • 163
1 vote
0 answers
93 views

Tensor equation problem (xact package)

So i want to solve the tensor equation P1[-μ,-ν]=0 with respect to A[r] and then B[r] but the problem is when hitting shift-enter the tensor given is way too long (if i press "show all" my ...
Stelios's user avatar
  • 11
1 vote
1 answer
242 views

Define a normalized vector field with xTensor

I just started to learn how to use xAct and xTensor. I would like to define the following vector field on a manifold equipped with a Lorentzian metric. My attempt was ...
Giulio Neri's user avatar
1 vote
1 answer
292 views

How to define a traceless tensor with xAct

I would like to define a tensor $A_i^j$ which is traceless ($A_i^i = 0$) and to obtain $A_i^j \delta^i_j = 0$ with xAct / xTensor / xCoba. I first tried defining an antisymmetric tensor, since they ...
gypsophila's user avatar
2 votes
1 answer
68 views

How to omit (not to display) the function arguments using TexAct package?

I try to use TexPrint command in the TexAct package, and the expression contains Derivative[1][f][r[]], H2[t[], r[]]etc., is it possible to avoid displaying these ...
Jh Wang's user avatar
  • 53
1 vote
0 answers
86 views

Lie derivative in xAct [closed]

I'm using xAct for calculation of Lie derivative of the metric g along the vector field $\zeta$: $$\mathcal{L}_\zeta g_{m n}$$ the metric g is: $$d s^2=e^{-2 t} d z d \bar{z}-d t^2$$ and $\zeta$: $$\...
独孤独's user avatar
4 votes
1 answer
255 views

Substitution rule is not working

I'm trying to replicate the equations of motion of the $4\partial$ST theory in Mathematica as is done in here as I need to use Mathematica and this package for my thesis. However, I have some trouble ...
Kabouter9's user avatar
  • 163
1 vote
0 answers
68 views

Traditional Output for Derivatives in the Components of xCoba's Lie Derivative

When using the xAct package xCoba to compute a Lie derivative, is there a simple way to adjust the accepted answer here (reproduced below) so that the components will display in the same way (eg $\...
Rosa Luxemberg's user avatar
3 votes
1 answer
260 views

Simplifying Expressions in xAct

I am completely new to xAct and was wondering if it is possible to tell xAct how to simplify expressions. Is there, for example, a way (e.g. in form of a supplied rule) to automatically simplify ...
olse barn's user avatar
3 votes
1 answer
296 views

xAct rule for antisymmetrization

using the xAct I'm trying to make a rule that the antisymmetrization in three indices of an expression goes to zero. Namely I have the killing vector $$ \xi^a $$ defined using ...
Nitaa a's user avatar
  • 770
4 votes
1 answer
88 views

xAct define normalization

I'm trying to get out some equations in the xAct suite. I would like to somehow define that the norm of a vector is a constant. ...
Nitaa a's user avatar
  • 770
4 votes
1 answer
345 views

How to define a Tensor with the symmetries like Riemann tensor?

I want to define a tensor that has the first two symmetries of Riemann tensor or maybe the last two. The symmetries of Riemann tensor are: 1) $ R_{\alpha\beta\gamma\lambda}=R_{\gamma\lambda\alpha\beta}...
Ali's user avatar
  • 131
0 votes
0 answers
69 views

in xAct, simplify output expression by specfic the form a function with ReplaceAll or Simplify

in xAct, at the beginning I define a function H1(t,r) that depends on two variables using the command DefScalarFunction, then I want to simplify an output ...
Jh Wang's user avatar
  • 53
1 vote
1 answer
316 views

xAct: How to identify and split module dummy indices?

Hi I'm using the package xAct but I'm running into an issue. It seems that before using //ChristoffelToGradMetric the christoffel connection has indices (which can ...
Tim's user avatar
  • 21
1 vote
1 answer
219 views

Counting multiple $-sign string indices in output and replacing them by normal indices

I'm using the package xTensor in xAct. My issue is that inside a module indices are replaced by strings of the form $##### which make the final output unreadable. In a related post Print expressions ...
Tim's user avatar
  • 21
2 votes
1 answer
265 views

Commutation of the partial derivatives on scalar in xAct

I do not know how to automatically commute partial derivatives on a scalar and simplify it. For example, if I have: $$\partial_a \partial_b \partial_c f- \partial_c \partial_a \partial_b f $$ where $f$...
Ali's user avatar
  • 131
4 votes
1 answer
149 views

Symbolic representation of large output

The package xAct does something really nice when it handles large outputs, which is to represent the expression as a symbol and display that symbol when the cursor hovers over it. For example, ...
shanedrum's user avatar
  • 587
2 votes
0 answers
172 views

How to use VarD to vary $\partial T$

I know that how the VarD works which is $ VarD[T, covd][expr] $. What about when I want to vary to a partial of a tensor ($\partial T)$? Let me say a simple question I wanted to test: $ L = \partial_{...
Ali's user avatar
  • 131
2 votes
1 answer
244 views

in xAct, how to set the components of a tensor to be zero

OBASuppose there is a vector $A^{a}$ appears in the result in different component form like $A^{\mu},A^{\nu},A^{\alpha}...$, I want all of them to be zero because the components of the tensor are zero,...
Jh Wang's user avatar
  • 53
3 votes
1 answer
129 views

how to split indices for a Spinor object?

I am wondering if anybody can help me with my question. My main relation is from gravity and is known as self-dual Riemann. When it is written in the Spinorial form it is like: $$G_{\mu \nu \alpha\...
Ali's user avatar
  • 131
1 vote
1 answer
337 views

xAct : how to define f to be a function of two variables?

f is a function of the coordinates x and y, how can I use the command DefScalarFunction to do this? ...
Jh Wang's user avatar
  • 53
0 votes
0 answers
291 views

calculate the component of a tensor-like quantity using xCoba,and how to use ContactBasis ,TraceBasisDummy

I am trying to do perturbation, it involved terms like this: $\partial_{l}(g^{lp} g^{kq} h_{pq}) (\partial_{i}g_{jk}) $ I want to obtain the simplified result of the components {i,j} all other indices ...
Jh Wang's user avatar
  • 53