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[tex] \mathcal L = \int dx^{4} \sqrt (-g) g^{ik}(\Gamma^{m}_{il}\Gamma^{l}_{km}-\Gamma^{l}_{ik}\Gamma^{m}_{lm}) [/tex]

from this and definition of 'Chrisstoffel symbols' the Lagrangian would be quadratic in the metric and its first derivatives , if we impose the constraint:

[tex] \mathcal{g}+1 =0 [/tex] (does it has any physical meaning??)

and a Qadratic Lagrangian in the derivatives and fields can be evaluated by means of a Functional integral.