Hamiltonian Analysis of 3-dimensional Spacetime in Bondi-like Coordinates

Abstract

The Hamiltonian analysis for a 3-dimensional connection dynamics of $\mathfrak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01},L_{02},L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the system is clearly presented. A null coframe with 3 independent variables and 9 connection coefficients are treated as basic configuration variables. All constraints and their consistency conditions, the solutions of Lagrange multipliers as well as the equations of motion are presented. There is no physical degree of freedom in the system. The Bañados-Teitelboim-Zanelli (BTZ) spacetime is discussed as an example to check the analysis. Unlike the ADM formalism, where only non-degenerate geometries on slices are dealt with and the Ashtekar formalism, where non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well, in the present formalism the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate.

13 pages

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Cited by in corpus (1)

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