GR is permissive theory in that it allows all sorts of crazy S-Ts and wild topologies.

-can start from Lagrangian basis; eqns are 2nd order and will be uniquely determined by generalized variables of Lagrange approach.
-Hamiltonian approach: transpose Euler-Lagrange eqns to Hamiltonian eqns of motion by introducing canonical momenta. Dependencies articulated by constrain eqns