Wavefunction of a Black Hole and the Dynamical Origin of Entropy

Details Wavefunction of a Black Hole and the Dynamical Origin of Entropy Wavefunction of a Black Hole and the Dynamical Origin of Entropy

1994-04-19

arxiv.org/abs/gr-qc/9404036v2

Phys.Rev.D51:1741-1763,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

39 pages, LaTeX misprint is corrected, original text is not modified

Scientific paper

10.1103/PhysRevD.51.1741

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.

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