Fuzzy Schwarzschild (2+1)-spacetime

TL;DR

This paper introduces a fuzzy Schwarzschild spacetime model as a noncommutative manifold, exploring quantum states, dynamics, and tunneling effects near a fuzzy black hole and proposing an extension to quantum wormholes.

Contribution

It presents a novel fuzzy Schwarzschild model incorporating quantum states, dynamics, and tunneling, extending noncommutative geometry to black hole and wormhole scenarios.

Findings

Quantum quasi-coherent states resemble classical Schwarzschild slices.

Fermion dynamics show decoherence near the fuzzy horizon.

Fermions can quantum tunnel through the fuzzy wormhole.

Abstract

We present a toy model of fuzzy Schwarzschild space slice (as a noncommutative manifold) which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of the $(r,\theta)$ Schwarzschild coordinates (the so-called Flamm's paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-coherent state and the deformation states of the noncommutative plane . The quantum dynamics of a fermion interacting with a fuzzy black hole described by the present model is studied. In particular we study the decoherence effects appearing in the neighborhood of the fuzzy event horizon. An extension of the model to describe a quantum wormhole is also proposed, where we show that fermions cross the wormhole not by traveling by its internal space but by quantum tunneling, in accordance with the non-traversable character of classical Einstein-Rosen bridges.