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We discuss the Hamiltonian formulation of gravity in 4-dimensional spacetimeunder Bondi-like coordinates{v, r, x^a, a=2, 3}. In Bondi-like coordinates, the3-dimensional hypersurface is a null hypersurface and the evolution directionis the advanced time v. The internal symmetry group SO(1,3) of the4-dimensional spacetime is decomposed into SO(1,1), SO(2), and T^\pm(2), whoseLie algebra so(1,3) is decomposed into so(1,1), so(2), t^\pm(2)correspondingly. The SO(1,1) symmetry is very obvious in this kind ofdecomposition, which is very useful in so(1,1) BF theory. General relativitycan be reformulated as the 4-dimensional coframe (e^I_\mu) and connection({\omega}^{IJ}_\mu) dynamics of gravity based on this kind of decomposition inthe Bondi-like coordinate system. The coframe consists of 2 null 1-forms e^-,e^+ and 2 spacelike 1-forms e^2, e^3. The Palatini action is used. TheHamiltonian analysis is conducted by the Dirac's methods. The consistencyanalysis of constraints has been done completely. There are 2 scalarconstraints and one 2-dimensional vector constraint. The torsion-freeconditions are acquired from the consistency conditions of the primaryconstraints about {\pi}^\mu_{IJ}. The consistency conditions of the primaryconstraints {\pi}^0_{IJ}=0 can be reformulated as Gauss constraints. Theconditions of the Lagrange multipliers have been acquired. The Poisson bracketsamong the constraints have been calculated. There are 46 constraints including6 first class constraints {\pi}^0_{IJ}=0 and 40 second class constraints. Thelocal physical degrees of freedom is 2. The integrability conditions ofLagrange multipliers n_0, l_0, and e^A_0 are Ricci identities. The equations ofmotion of the canonical variables have also been shown.

Hamiltonian Analysis of 4-dimensional Spacetime in Bondi-like Coordinates