Quantum dynamics of the Einstein-Rosen wormhole throat

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.044022· OSTI ID:21504988

Kunstatter, Gabor; Peltola, Ari ^[1]; Louko, Jorma ^[2]

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1. Department of Physics and Winnipeg Institute for Theoretical Physics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba, R3B 2E9 (Canada)
2. School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)

We consider the polymer quantization of the Einstein wormhole throat theory for an eternal Schwarzschild black hole. We numerically solve the difference equation describing the quantum evolution of an initially Gaussian, semiclassical wave packet. As expected from previous work on loop quantum cosmology, the wave packet remains semiclassical until it nears the classical singularity at which point it enters a quantum regime in which the fluctuations become large. The expectation value of the radius reaches a minimum as the wave packet is reflected from the origin and emerges to form a near-Gaussian but asymmetrical semiclassical state at late times. The value of the minimum depends in a nontrivial way on the initial mass/energy of the pulse, its width, and the polymerization scale. For wave packets that are sufficiently narrow near the bounce, the semiclassical bounce radius is obtained. Although the numerics become difficult to control in this limit, we argue that for pulses of finite width the bounce persists as the polymerization scale goes to zero, suggesting that in this model the loop quantum gravity effects mimicked by polymer quantization do not play a crucial role in the quantum bounce.

• OSTI ID: 21504988
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevD.83.044022; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COSMOLOGY
EXPECTATION VALUE
FLUCTUATIONS
GENERAL RELATIVITY THEORY
MASS
NUMERICAL SOLUTION
PULSES
QUANTIZATION
QUANTUM GRAVITY
SCHWARZSCHILD METRIC
SEMICLASSICAL APPROXIMATION
SINGULARITY
WAVE PACKETS
APPROXIMATIONS
CALCULATION METHODS
FIELD THEORIES
MATHEMATICAL SOLUTIONS
METRICS
QUANTUM FIELD THEORY
RELATIVITY THEORY
VARIATIONS