Black holes and Rindler superspace: Classical singularity and quantum unitarity

Journal Article · Mon Oct 15 00:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.084004· OSTI ID:21032451

Chou, C -H; Yu, H -L ^[1]; Soo, C ^[2]

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1. Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan (China)
2. Department of Physics, National Cheng Kung University, Tainan, Taiwan (China)

Canonical quantization of spherically symmetric initial data appropriate to classical interior black hole solutions in four dimensions is solved exactly without gauge fixing the remaining kinematic Gauss law constraint. The resultant mini-superspace manifold is two dimensional, of signature (+,-), nonsingular, and can be identified with the first Rindler wedge. The associated Wheeler-DeWitt equation with evolution in intrinsic superspace time is a free massive Klein-Gordon equation, and the Hamilton-Jacobi semiclassical limit of plane wave solutions can be matched to the interiors of Schwarzschild black holes. Classical black hole horizons and singularities correspond to the boundaries of the Rindler wedge. Exact wave functions of the Dirac equation in superspace are also considered. Precise correspondence between Schwarzschild black holes and free-particle mechanics in superspace is noted. Despite the presence of classical singularities, Hermiticity of the Dirac Hamiltonian operator, and thus unitarity of the quantum theory, is equivalent to an appropriate boundary condition which must be satisfied by the quantum states. This boundary condition holds for quite generic quantum wave packets of energy eigenstates, but fails for the usual Rindler fermion modes which are eigenstates with zero uncertainty in energy.

• OSTI ID: 21032451
• Journal Information: Physical Review. D, Particles Fields, Vol. 76, Issue 8; Other Information: DOI: 10.1103/PhysRevD.76.084004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
BOUNDARY CONDITIONS
DIRAC EQUATION
EIGENFUNCTIONS
EIGENSTATES
EIGENVALUES
FERMIONS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
KLEIN-GORDON EQUATION
MATHEMATICAL SOLUTIONS
QUANTIZATION
SCHWARZSCHILD METRIC
SEMICLASSICAL APPROXIMATION
SINGULARITY
TWO-DIMENSIONAL CALCULATIONS
UNITARITY
WAVE FUNCTIONS
WAVE PACKETS
WAVE PROPAGATION