engleski

Quantum Horizon and Space-Time Non-Commutativity

In standard general relativity without quantum mechanics (QM) a fundamental instability against collapse implies the existence of black holes as stable solutions of Einstein's equations.The QM and the QFT ( quantum field theory ) in the curved spacetime with classical event horizon are troubled by the singularity at the horizon.This problem may be solved by treating the black hole as a quantum state which implies that the energy of the black hole and its corresponding time do not commute at the horizon.In this picture we study the 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 the time operator near-horizon is given and its self-adjointness discussed.

black holes; quantum horizon; time operator

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