Quantum dynamics of the Einstein-Rosen wormhole throat

TL;DR

This paper explores the quantum behavior of the Einstein-Rosen wormhole throat using polymer quantization, revealing a quantum bounce that prevents singularity formation and depends on initial conditions.

Contribution

It provides a numerical analysis of the quantum evolution of the wormhole throat, demonstrating the persistence of the bounce across different parameters and the limited role of loop quantum gravity effects.

Findings

Wave packet remains semi-classical until near the singularity

Quantum bounce occurs, preventing singularity formation

Bounce radius depends on initial mass, width, and polymerization scale

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.