Indefinite oscillators and black-hole evaporation

Details Indefinite oscillators and black-hole evaporation Indefinite oscillators and black-hole evaporation

2008-12-15

arxiv.org/abs/0812.2848v3

Annalen der Physik 18, 722-735 (2009)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 6 figures, conceptual clarifications added, final version

Scientific paper

10.1002/andp.200910366

We discuss the dynamics of two harmonic oscillators of which one has a negative kinetic term. This model mimics the Hamiltonian in quantum geometrodynamics, which possesses an indefinite kinetic term. We solve for the time evolution in both the uncoupled and coupled case. We use this setting as a toy model for studying some possible aspects of the final stage of black-hole evaporation. We assume that one oscillator mimics the black hole, while the other mimics Hawking radiation. In the uncoupled case, the negative term leads to a squeezing of the quantum state, while in the coupled case, which includes back reaction, we get a strong entangled state between the mimicked black hole and the radiation. We discuss the meaning of this state. We end by analyzing the limits of this model and its relation to more fundamental approaches.

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