Space-Time Non-Commutativity near Horizon of a Black Hole

Details Space-Time Non-Commutativity near Horizon of a Black Hole Space-Time Non-Commutativity near Horizon of a Black Hole

2005-02-25

arxiv.org/abs/gr-qc/0502111v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, LaTex

Scientific paper

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.

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