Thermal time of noncommutative Minkowski spacetime

TL;DR

This paper investigates the thermal time hypothesis within noncommutative Minkowski spacetimes, revealing how modular groups relate to different deformations and their implications for quantum gravity phenomenology.

Contribution

It demonstrates the emergence of natural modular groups in noncommutative Minkowski spacetimes and explores their physical significance, especially in $$-Minkowski and $ ho$-Minkowski cases.

Findings

Thermal time flow corresponds to time translation in $$-Minkowski.

Absence of thermal time in $ ho$-Minkowski relates to its discrete global time.

Discussion on implications for quantum gravity phenomenology.

Abstract

In this paper, we study the thermal time hypothesis of arXiv:gr-qc/9406019 in the context of noncommutative deformations of Minkowski. We show that a natural modular group arises from the modular function of the momentum space. In the specific case of $\kappa$-Minkowski, we show that this thermal time flow corresponds to the globally defined time coordinate translation. On the other hand, the absence of thermal time for $\rho$-Minkowski is directly related to the discreteness of its global time. The impact of inner automorphism transformation on the physics and the treatment of unimodular case (unthermalised spacetimes) are discussed. Moreover, a reflection on the use of thermal field theory for quantum gravity phenomenology is put forward, as we just bridged thermal spacetimes with $\kappa$-Minkowski, often considered a "flat limit" of a quantum gravity candidate theory.