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

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.