Indefinite oscillators and black-hole evaporation

TL;DR

This paper models black-hole evaporation using a toy system of two harmonic oscillators with one having negative kinetic energy, revealing insights into quantum state squeezing and entanglement during black-hole evaporation.

Contribution

It introduces a simplified oscillator model with indefinite kinetic terms to study black-hole evaporation dynamics and quantum entanglement effects.

Findings

Negative kinetic term causes quantum state squeezing.

Coupled oscillators produce strong entanglement.

Model provides insights into black-hole radiation and back reaction.

Abstract

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.