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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 $g_{\mu\nu}$ is the first metric, $\bar{g}_{\mu\nu}$ is the second metric, $\phi$ is a scalar field and $\nabla_\mu$ is the covariant derivative, $\mu$ and $\nu$ are both abstract indices.

For the simpler conformal transformation relation

$\qquad \bar{g}_{\mu\nu}=A(\phi) g_{\mu\nu} ,$

I can use the following code 

<< xAct`xTensor`
DefManifold[M, 4, {a, b, c, d, e, f}]
DefMetric[-1, g[-a, -b], CD, {";", "\[Del]"}]
DefTensor[A[], M]
DefMetric[-1,gbar[-a,-b],cd,{"|", "||"},ConformalTo->{g[-a,-b],A[]}]

to achieve it.

But I don't know how to define the disformal transformation relation between two metrics.

I will really appreciate it if someone helps me!

Zhu Yi
  • 11
  • 3
  • https://mathematica.stackexchange.com/questions/69423/how-can-i-define-a-metric-in-xact – nufaie Mar 29 '19 at 14:41
  • https://mathematica.stackexchange.com/questions/154612/how-to-apply-perturbed-metric-in-xpert-calculations – nufaie Mar 29 '19 at 14:41

0 Answers0