  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.
