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Tagged with adm-formalism lagrangian-formalism
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ADM Formalism for the Effective String Theory
We will consider the following effective action of string theory in leading order of $\alpha'$:
$$S=\frac{1}{2\kappa^2_0}\int d^{D}X\sqrt{-G}e^{-2\Phi}\left[R-2\Lambda-\frac{1}{12}H_{\mu\nu\lambda}H^{\...
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Setting $N=1$ and $N^a=0$ in the Einstein-Hilbert action
In the ADM formalism of general relativity, one obtains a $3+1$ split of spacetime by setting $$\mathrm d s^2=(-N^2+N_a N^a) \,\mathrm d t^2 + 2N_a\,\mathrm d t\,\mathrm d x^a + q_{ab} \,\mathrm d x^a\...
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