All Questions
38
questions
1
vote
0
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43
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Calculate and transfrom the metric to the orthonormal frame
Let's suppose, the line element is like this:
$$ds^2 = -a^2(1+2\psi)d\tau^2 - 2a^2 B_idx^i d\tau + a^2(1-2\phi)(dx^2 + dy^2 + dz^2)$$
I like to get the output of the metric components from it, ...
- 149
1
vote
0
answers
39
views
Package for calculating ADM mass for a given asymptotically flat metric tensor
I am asking for Mathematica package, such that for the input of an asymptotically flat Lorentzian metric tensor $g_{\mu\nu}$ it will give the ADM mass of the object that creates the corresponding ...
1
vote
1
answer
101
views
Metric tensor coordinate transformation with off-diagonal components
I know there is already an answer for this type of question given here: Computing the metric tensor under a coordinate transformation but the answer is not satisfactory as it is not clear to me how I ...
- 123
0
votes
1
answer
162
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A code to calculate Einstein tensor [duplicate]
I use the following MA code to calculate Einstein’s tensor. I’m asking about the zero component of the Einstein’s tensor, is it correct?
Because I think $G_{00}$ should contains the terms in the zero ...
- 287
0
votes
0
answers
53
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Calculating and collecting the terms of the zero component of the Einstein’s tensor
I try to calculate the $G_{00}$ of the Einstein tensor
$G_{\mu\nu}= R_{\mu\nu} -\frac{1}{2} g_{\mu\nu} R$
for the metric:
$g_{00}=-a^2(\tau)\left( 1+2 \phi^{(n)}\right),$
$g_{0i} = a^2(\tau)\left( \...
- 287
0
votes
0
answers
77
views
How to calculate Einstein tensor components for this metric?
I try to calculate the Einstein tensor compenents from the eqution:
$
G_{\alpha\beta} = \frac{\nabla_\beta (\partial_\alpha \phi)}{\phi} - \frac{1}{2\phi^2} \left[ \frac{\partial_4 \phi \partial_4 g_{\...
- 287
0
votes
0
answers
131
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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:
...
- 287
0
votes
0
answers
164
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Simplifying the Einstein tensor in case of a perturbed FRW metric
I use the code in this thread's answer:
(Calculating Einstein tensor components in Kaluza-Klein model)
to get the Einstein tensor components of a four-dimensional Kaluza Klein model.
But instead of ...
- 287
1
vote
1
answer
212
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Calculating Einstein tensor components in Kaluza-Klein model
I try to calculate the Einstein tensor of Kaluza-Klein model from this paper. It is given by Equation (55)
$
G_{\alpha\beta} = \frac{\nabla_\beta (\partial_\alpha \phi)}{\phi} - \frac{1}{2\phi^2} \...
- 287
4
votes
1
answer
1k
views
What are some Mathematica packages used for general relativity?
Could you suggest any Mathematica packages that are used for General relativity calculations? Id like to write code to solve the Schwarzchild Lagrangian equation.
2
votes
0
answers
156
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 ...
- 21
1
vote
1
answer
134
views
TensoriaCalc does not display the correct output
I am trying to use TensoriaCalc to calculate the components of the Ricci and the Riemann tensor of the following metric: $R^{2} \left(d\theta^{2} + \sin^{2}\left(\theta \right)d\phi^{2} \right)$;
...
- 113
2
votes
1
answer
124
views
Pathological expression for field strength contractions in a curved background
I am trying to define in Mathematica the quantity $\star F^{\mu}=\frac{1}{2}\epsilon^{\mu\alpha\beta}F_{\alpha\beta}$, where $F_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu+\left[A_\mu,A_\nu\right]$. ...
- 135
2
votes
0
answers
37
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Simulation of Quantum pseudo-telepathy
I would like to mathematically simulate Quantum pseudo-telepathy on The magic square game from Wikipedia.
In section Pseudo-telepathic strategies we can read:
The trick is for Alice and Bob to share ...
- 20.1k
0
votes
1
answer
269
views
Is there a way of calculating Expectation Values of tensor operators in Mathematica?
This Wikipedia article in on Bell's Theorem lists a whole bunch of expectation values for Bell states:
$$\langle A_0 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_0 \otimes B_1 \rangle = \frac{1}...
- 243