Accelerated horizons and Planck-scale kinematics

TL;DR

This paper explores how Planck-scale deformations of relativistic kinematics affect accelerated horizons, revealing finite blueshift effects and implications for horizon entropy, with Lorentz invariance violations necessary for consistent mode densities.

Contribution

It extends the concept of accelerated horizons to deformed relativistic kinematics, analyzing effects on blueshift and horizon entropy at the Planck scale.

Findings

Finite blueshift observed near horizons due to symmetry deformation

Lorentz invariance violation needed for non-diverging mode density

Potential implications for horizon entropy calculations

Abstract

We extend the concept of accelerated horizons to the framework of deformed relativistic kinematics at the Planck scale. We show that the non-trivial effects due to symmetry deformation manifest in a finite blueshift for field modes as measured by a Rindler observer approaching the horizon. We investigate whether, at a field theoretic level, this effect could manifest in the possibility of a finite horizon contribution to the entropy, a sort of covariant brick-wall. In the specific model of symmetry deformation considered it will turn out that a non-diverging density of modes close to the horizon can be achieved only by introducing a momentum space measure which violates Lorentz invariance.