Wavefunction of a Black Hole and the Dynamical Origin of Entropy
Apr 22, 1994
39 pages
Published in:
- Phys.Rev.D 51 (1995) 1741-1763
e-Print:
- gr-qc/9404036 [gr-qc]
Report number:
- ALBERTA-THY-13-94
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Abstract: (arXiv)
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.- general relativity
- black hole: wave function
- thermodynamics
- path integral
- boundary condition
- vacuum state
- entropy
- effective action
- bibliography
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