  This is a contribution to MG9 session BHT4. Certain geometrically
distinguished frame on a non-expanding horizon and in its space-time
neighborhood, as well as the Bondi-like coordinates are constructed. The
construction provides free degrees of freedom, invariants, and the existence
conditions for a Killing vector field. The reported results come from the joint
works with Ashtekar and Beetle.

General Relativity and Quantum Cosmology