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The Chern-Simons lagrangian density in the space of metrics of a3-dimensional manifold M is not invariant under the action of diffeomorphismson M. However, its Euler-Lagrange operator can be identified with the Cottontensor, which is invariant under diffeomorphims. As the lagrangian is notinvariant, Noether Theorem cannot be applied to obtain conserved currents. Weshow that it is possible to obtain an equivariant conserved current for theCotton tensor by using the first equivariant Pontryagin form on the bundle ofmetrics. Finally we define a hamiltonian current which gives the contributionof the Chern-Simons term to the black hole entropy, energy and angularmomentum.

Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms