2005/02/25 by M. Martinis, Martinis, M., Vesna Mikuta-Martinis +2
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0502111
7 pages, LaTex
arxiv created 2005/02/25 · arxiv updated 2009/12/01
We consider dynamics of a quantum scalar field, minimally coupled to classical gravity, in the near-horizon region of a Schwarzschild black-hole. It is described by a static Klein-Gordon operator which in the near-horizon region reduces to a scale invariant Hamiltonian of the system. This Hamiltonian is not essentially self-adjoint, but it admits a one-parameter family of self-adjoint extension. The time-energy uncertainty relation, which can be related to the thermal black-hole mass fluctuations, requires explicit construction of a time operator near-horizon. We present its derivation in terms of generators of the affine group. Matrix elements involving the time operator should be evaluated in the affine coherent state representation.