Wavefunction of a Black Hole and the Dynamical Origin of Entropy
A. O. Barvinsky, V. P. Frolov, A. I. Zelnikov
TL;DR
The paper proposes that black-hole entropy arises from dynamical interior degrees of freedom by formulating a no-boundary wavefunction on an Einstein–Rosen bridge and showing that, semiclassically, interior perturbations reproduce the Hartle–Hawking vacuum for all spins. By tracing over exterior degrees of freedom, it derives a one-loop entropy that is divergent near the horizon, suggesting horizon fluctuations provide the necessary UV cutoff to recover the area law universality. The work connects a covariant interior-field description with Euclidean and effective-action approaches, arguing that horizon zitterbewegung is essential to obtain a finite, universal entropy, and discusses limitations of renormalization-based pictures. Overall, it links the dynamical microstructure of the black hole interior to its thermodynamic behavior through a consistent quantum-gravity framework.
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.