How Does ADM Formalism Lead to Equation 11 in the Context of General Relativity?

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Dear all,
I have a problem understanding ADM formalism. In a paper I am reading (cited as arXiv:1003.2635v2 [hep-ph]) it is said that ADM metric is as below:

ds2 = −N2dt2 + hij (dxi + Nidt)(dxj + Njdt)

and from this metric is has reached to equation 11 of the article.

how can I reach to this equation (11)?

please help!
 
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Can you upload the article for us to have a look at?
 
of course.
this is the article
thanks for your time...
 

Attachments

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
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Thread 'Help to convert units of a simple formula'

The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
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