Wavefunction of a Black Hole and the Dynamical Origin of Entropy

TL;DR

This paper develops a quantum wave function approach to black hole entropy, proposing a no-boundary formalism that relates internal states to entropy, potentially resolving divergence issues through horizon fluctuations.

Contribution

It introduces a no-boundary wave function for black holes and links internal quantum states to finite entropy via horizon fluctuations.

Findings

Wave function coincides with Hartle-Hawking vacuum in small perturbations

Density matrix of internal black hole states is derived

Horizon quantum fluctuations may regularize entropy divergence

Abstract

Recently it was proposed to explain the dynamical origin of the entropy of a black hole by identifying its dynamical degrees of freedom with states of quantum fields propagating in the black-hole's interior. The present paper contains the further development of this approach. The no-boundary proposal (analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is put forward for defining the wave function of a black hole. This wave function is a functional on the configuration space of physical fields (including the gravitational one) on the three-dimensional space with the Einstein-Rosen bridge topology.It is shown that in the limit of small perturbations on the Kruskal background geometry the no-boundary wave function coincides with the Hartle-Hawking vacuum state. The invariant definition of inside and outside modes is proposed. The density matrix describing the internal state of a black hole is obtained by averaging over the outside modes. This density matrix is used to define the entropy of a black hole, which is to be divergent. It is argued that the quantum fluctuations of the horizon which are internally present in the proposed formalism may give the necessary cut-off and provide a black hole with the finite entropy.