Can Effects of a Generalized Uncertainty Principle Appear in Compact Stars?

TL;DR

This paper investigates how a generalized uncertainty principle with a minimum length could influence the physics of compact stars, specifically neutron stars, potentially explaining observed mass-radius relations.

Contribution

It introduces a novel approach to incorporate GUP effects into semiclassical models of neutron stars using a deformation transformation.

Findings

GUP effects lead to equations of state compatible with observed neutron star masses.

Maximum neutron star mass around 2.5 solar masses with radii near 12 km.

Results suggest the noncommutative scale is very small.

Abstract

In the present contribution, a preliminary analysis of the effects of the Generalized Uncertainty Principle (GUP) with a minimum length, in the context of compact stars, is performed. On basis of a deformed Poisson canonical algebra with a parametrized minimum length scale that induces deviations from conventional Quantum Mechanics, fundamental questions involving the consistence, evidences and proofs of this approach as a possible cure for unbounded energy divergence are outlined. The incorporation of GUP effects into semiclassical 2N-dimensional systems is made by means of a time-invariant distortion transformation applied to their non-deformed counterparts. Assuming the quantum hadrodynamics $\sigma-\omega$ approach as a toy-model, due to its simplicity and structured description of neutron stars, we perform a preliminary analysis of GUP effects with a minimum spacetime length on these compact objects. The corresponding results for the equation of state and the mass-radius relation for neutron stars are in tune with recent observations with a maximum mass around $2.5 M_{\odot}$ and radius close to $12$ km. Our results also indicate the smallness of the noncommutative scale.