Abstract

Asymptotically anti-de Sitter spaces are defined by boundary conditions on the gravitational field which obey the following criteria: (i) they are 0(3, 2) invariant; (ii) they make the 0(3, 2) surface integral charges finite; (iii) they include the Kerr-anti-de Sitter metric. An explicit expression of the O (3, 2) charges in terms of the canonical variables is given. These charges are shown to close in the Dirac brackets according to the anti-de Sitter algebra. The results are extended to the case of N = 1 supergravity. The coupling to gravity of a third-rank, completely antisymmetric, abelian gauge field is also considered. That coupling makes it possible to vary the cosmological constant and to compare the various anti-de Sitter spaces which are shown to have the same energy.