(adsbygoogle = window.adsbygoogle || []).push({}); Gauss-Bonnet term extrinsic curvature calculations?

In General Relativity if one wants to calculate the field equation with surface term, must use this equation:

S=[itex]\frac{1}{16\pi G}[/itex][itex]\int\sqrt{-g} R d^{4} x[/itex]+[itex]\frac{1}{8\pi G}[/itex][itex]\int\sqrt{-h} K d^{3} x[/itex]

The second term is so-called Gibbons-Hawking boundary term and K is extrinsic curvature.

If one is about to use another Lagrangian, for instance Gauss-Bonnet term, must calculate the new extrinsic curvature, K, associated with this new Lagrangian.

I want to know is there a standard method for calculating K?

I would be grateful if anybody can help me in learning this procedure. Please introduce references if you know some.

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# Gauss-Bonnet term extrinsic curvature

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