2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35133We study dynamics of a scalar field in the near-horizon region described by a static Klein-Gordon operator which is the Hamiltonian of the system. The explicite construction of a time operator near-horizon is given and its self-adjointness discussed.LaTex, 6 pages, no figures, Expanded version of a poster presented at 5 European Advanced Study Conference in Ancient Olympia, Greece, July 2004. to appear in a special issue of IJBCGeneral Relativity and Quantum Cosmologytext