Compressibility Function and Speed of Sound in the Non-Commutative Quantum Hadrodynamics Type-I Model for Neutron Stars

We investigate the effects of a minimal measurable length on neutron stars, within the quantum hadrodynamics (QHD-I) model modified by the Generalized Uncertainty Principle (GUP). Working in a deformed Poisson algebra framework, we incorporate GUP effects via a time-invariant transformation of the phase space volume, effectively reducing the number of accessible quantum states at high momentum. We focus specifically on two observables critical to this star physics, the compressibility, which encapsulates how stiff EOS become, and the speed of sound, which imposes a causality constraint. Using this model as an exploratory study, due to its simplicity and structured description, we perform a preliminary analysis of GUP effects with a minimum spacetime length on these compact objects. This deformation increases the speed of sound while decreasing the compressibility, and we identify critical values of the Fermi momentum beyond which both quantities become nonphysical. These results underscore the potential role of a minimal length scale in shaping the bulk properties and possible phase structures of dense matter in neutron stars.