Questions tagged [xact]
Questions about xAct, a suite of packages for tensor computer algebra, which includes the packages xCore, xPerm, xTensor, and xCoba.
123
questions
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17
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Tensors without explicit specifications in xCoba
In the standard Schwarzschild setup I have the following tensor:
...
-1
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0
answers
27
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Specify a tensor or a function with a specific form in xCoba [closed]
Suppose, in the Schwarzschild geometry with the standard coordinates, I wanted to specify an electromagnetic tensor F with the (six) components all being functions of r: A(r), B(r), C(r), D(r), G(r), ...
1
vote
1
answer
103
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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 ...
1
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0
answers
34
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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:
...
2
votes
1
answer
70
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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^...
- 147
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0
answers
33
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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 ...
- 29
0
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0
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79
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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:
...
- 213
1
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0
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35
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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?...
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2
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0
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80
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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 ...
2
votes
0
answers
108
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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 ...
- 21
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68
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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 ...
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0
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85
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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 ...
1
vote
0
answers
100
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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 ...
- 165
2
votes
0
answers
116
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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 ...
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0
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161
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[xAct][xCoba] Derive Metric Related Quantities like Riemann/Ricci Tensor/Scalar, Det(g), Christoffel Symbols
I'd like to prepare a mathematica notebook, where I can define a metric and derive quantities like the Riemann tensor, the Ricci tensor, the Ricci scalar, the determinant of the metric and the various ...
- 181
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0
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117
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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
...
- 11
1
vote
0
answers
58
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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?
...
- 11
1
vote
1
answer
72
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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 ...
- 166
3
votes
1
answer
89
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 ...
- 823
2
votes
1
answer
154
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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 ...
- 823
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0
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72
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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)}\...
- 163
2
votes
0
answers
240
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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 ...
- 377
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59
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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 ...
2
votes
1
answer
229
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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$ ...
- 163
1
vote
0
answers
73
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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 ...
- 11
1
vote
1
answer
157
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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
...
- 13
1
vote
1
answer
199
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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 ...
- 386
1
vote
1
answer
56
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 ...
- 43
1
vote
0
answers
69
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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$$
and $\zeta$:
$$\...
- 11
4
votes
1
answer
234
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 ...
- 163
1
vote
0
answers
52
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 $\...
3
votes
1
answer
189
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 ...
- 91
2
votes
1
answer
216
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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 ...
- 698
4
votes
1
answer
81
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.
...
- 698
4
votes
1
answer
268
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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}...
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0
answers
50
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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 ...
- 43
1
vote
1
answer
221
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 ...
- 21
1
vote
1
answer
167
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 ...
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2
votes
1
answer
180
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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 $f$...
- 131
3
votes
1
answer
133
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,
...
- 557
2
votes
0
answers
158
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_{...
- 131
2
votes
1
answer
209
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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,...
- 43
3
votes
1
answer
117
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\...
- 131
1
vote
1
answer
250
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?
...
- 43
0
votes
0
answers
218
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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 ...
- 43
0
votes
1
answer
39
views
"Uncaught Throw[Null]","VBundleOfMetric" and "MetricsOfVBundle" when using package "xAct"
The codes are below:
Remove["Global`*"]
Then:
...
5
votes
0
answers
284
views
Manipulating tensorial terms with xAct, ToCanonical is not perfoming well
I am trying to calculate perturbations of some complicated Lagrangians. Using xAct and more specifically VarD to perform the perturbations the expressions become ...
- 51
2
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0
answers
166
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Not able to impose rules on xPert perturbations
Whenever I try to define rules to xPert perturbations, they seem not to work at all. For instance, I am interested in considering traceless and divergence-free perturbations and defining
...
1
vote
0
answers
132
views
xAct tensor product
I am a beginner of xAct for computation in GR. I am doing component computation in specified charts, and quite often I need to extract the list of components by the function ...
- 111
2
votes
2
answers
952
views
xAct xCoba: How to extract components of CTensors correctly
I'm working in a specific chart ch with a metric and associated covariant derivative cd:
...
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