Hamiltonian of General Relativity

[Physicist97]

Pretty straightforward question. The Einstein-Hilbert Action says that the Lagrangian for Gravity is $L=R(-g)^{1/2}$ where $g$ is the determinant of the Metric Tensor and $R$ is the Ricci Scalar (Actually I am not sure if the determinant of the metric should be included there). From this is it possible to find a Hamiltonian for General Relativity?

 

[PeterDonis]

From this is it possible to find a Hamiltonian for General Relativity?

Yes, but you pay a stiff price for it: to derive a Hamiltonian formulation, you have to pick a particular split of spacetime into space and time. See, for example, here:

https://en.wikipedia.org/wiki/Hamiltonian_constraint#Hamiltonian_of_classical_general_relativity