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I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the(2,2) formalism without assuming isometries. In this formalism, quasi-localenergy, linear momentum, and angular momentum are identified from the fourEinstein's equations of the divergence-type, and are expressed geometrically interms of the area of a two-surface and a pair of null vector fields on thatsurface. The associated quasi-local balance equations are spelled out, and thecorresponding fluxes are found to assume the canonical form of energy-momentumflux as in standard field theories. The remaining non-divergence-typeEinstein's equations turn out to be the Hamilton's equations of motion, whichare derivable from the {\it non-vanishing} Hamiltonian by the variationalprinciple. The Hamilton's equations are the evolution equations along theout-going null geodesic whose {\it affine} parameter serves as the timefunction. In the asymptotic region of asymptotically flat spacetimes, it isshown that the quasi-local quantities reduce to the Bondi energy, linearmomentum, and angular momentum, and the corresponding fluxes become the Bondifluxes. The quasi-local angular momentum turns out to be zero for anytwo-surface in the flat Minkowski spacetime. I also present a candidate forquasi-local {\it rotational} energy which agrees with the Carter's constant inthe asymptotic region of the Kerr spacetime. Finally, a simple relation betweenenergy-flux and angular momentum-flux of a generic gravitational radiation isdiscussed, whose existence reflects the fact that energy-flux alwaysaccompanies angular momentum-flux unless the flux is an s-wave.Comment: 36 pages, 3 figures, RevTex

New Hamiltonian formalism and quasilocal conservation equations of general relativity