Explicitly evaluating perturbation equations

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Jamal Shafiq

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Dec 9, 2014, 3:21:00 AM12/9/14
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I have defined a manifold, along with a metric and its perturbation. Using the Perturbed[] command I've been able to compute the perturbation of the Ricci tensor to all orders, but how do I actually 'plug in' a background metric, and explicitly carry out the derivatives and all summations? It's going to be quite messy, so is there a way to specify an ansatz for the perturbation?

I tried using Bloomfield's tutorial on perturbation theory with xAct on xAct.es but it only goes as far as using Perturbed[].


Obinna Umeh

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Dec 12, 2014, 1:49:21 AM12/12/14
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Hi Jamal,

What type of background metric are you interested in? If it is a homogeneous background like the FLRW metric, you could use xPand to do your calculation. xPand has a detailed documentation on how to use it.


Obinna

On Tue, Dec 9, 2014 at 10:21 AM, Jamal Shafiq <00ja...@sis.gl> wrote:
I have defined a manifold, along with a metric and its perturbation. Using the Perturbed[] command I've been able to compute the perturbation of the Ricci tensor to all orders, but how do I actually 'plug in' a background metric, and explicitly carry out the derivatives and all summations? It's going to be quite messy, so is there a way to specify an ansatz for the perturbation?

I tried using Bloomfield's tutorial on perturbation theory with xAct on xAct.es but it only goes as far as using Perturbed[].


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Jamal Shafiq

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Dec 12, 2014, 3:12:58 AM12/12/14
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Thank you for your reply. My background is a solution to low energy effective bosonic string theory, so I don't think using xPand is an option.
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