Quantum dynamics of the Einstein-Rosen wormhole throat

Abstract

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, semi-classical wave packet. As expected from previous work on loop quantum cosmology, the wave packet remains semi-classical 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 semi-classical state at late times. The value of the minimum depends in a non-trivial 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 semi-classical 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.

23 pages, 11 figures. v2: minor corrections and clarifications

References in corpus (16)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Loop Quantum Dynamics of the Schwarzschild Interior
• Loop quantum cosmology and the k = - 1 RW model
• Black holes in loop quantum gravity: the complete space-time
• Is loop quantization in cosmology unique?
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Black hole interior from loop quantum gravity
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
• Complete, Single-Horizon Quantum Corrected Black Hole Spacetime
• Quantum gravity and the Coulomb potential
• Polymer quantization, singularity resolution and the 1/r^2 potential
• Stability of the Schwarzschild Interior in Loop Quantum Gravity
• Semiclassical states for quantum cosmology
• Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology