Quantum Field, Thermodynamics and Black Hole on Coherent State Representation of Fuzzy Space

TL;DR

This paper explores fuzzy space using coherent states, revealing smeared particles, modified propagators, and black hole properties, including maximum temperature and stable remnants, extending noncommutative geometry concepts to quantum gravity and thermodynamics.

Contribution

It introduces a coherent state formalism for fuzzy space, deriving new particle smearing functions and analyzing black hole thermodynamics and stability within this framework.

Findings

Fuzziness replaces point particles with smeared exponential decay sources.

Black holes in fuzzy space reach a maximum temperature and leave stable remnants.

The study extends noncommutative geometry to quantum gravity and black hole physics.

Abstract

We first use the coherent state formalism of fuzzy space to show that the fuzziness will eliminate point-like structure of a particle in favor of smeared object, which is an exponential decay function in contrast to the Gaussian type in the Moyal noncommutative space. The exponential decay function implies that, in the UV region, the fuzziness provides an extra power-decay factor in the Feynman propagator, contrasts to the exponential-decay factor in the Moyal space. We also calculate the particle heat capacity and see that it approaches to zero at high temperature. Next, we use the found smeared source to study the Schwarzschild-like geometry and see that the black hole can reach a finite maximum temperature before cooling down to absolute zero and leave a stable remnant, as that in the noncommutative case. The properties of fuzzy 3D BTZ and the fuzzy Kaluza-Klein black holes are also discussed. Finally, we present a criterion for existence a regular black hole with a general smeared source function.