2 research outputs found
Quantum Structure of Space Near a Black Hole Horizon
We describe a midi-superspace quantization scheme for generic single horizon
black holes in which only the spatial diffeomorphisms are fixed. The remaining
Hamiltonian constraint yields an infinite set of decoupled eigenvalue
equations: one at each spatial point. The corresponding operator at each point
is the product of the outgoing and ingoing null convergences, and describes the
scale invariant quantum mechanics of a particle moving in an attractive
potential. The variable that is analoguous to particle position is the
square root of the conformal mode of the metric. We quantize the theory via
Bohr quantization, which by construction turns the Hamiltonian constraint
eigenvalue equation into a finite difference equation. The resulting spectrum
gives rise to a discrete spatial topology exterior to the horizon. The spectrum
approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur