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

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The discussion centers on the ADM formalism in the context of General Relativity, specifically referencing the metric provided in the paper arXiv:1003.2635v2 [hep-ph]. The ADM metric is defined as ds² = −N²dt² + hij (dxi + Nidt)(dxj + Njdt). Participants seek clarification on how to derive equation 11 from this metric, indicating a need for a deeper understanding of the ADM formalism and its applications in theoretical physics.

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shadi_s10
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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...
 

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