Maximum Momentum, Minimal Length and Quantum Gravity Effects of Compact Star Cores

Based on the generalized uncertainty principle with maximum momentum and minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited. Applying this equation of state to the Tolman–Oppenheimer–Volkoff (TOV) equation, the quantum gravitational effects on the cores of compact stars are discussed. In the center of compact stars, we obtain the singularity-free solution of the metric component, g_\rm tt\sim -(1+0.2185\times \tilde r^2). By numerically solving the TOV equation, we find that quantum gravity plays an important role in the region r\sim 10^4\alpha_0(\Delta x)_\min. Current observed masses of neutron stars indicate that the dimensionless parameter \alpha_0 cannot exceed 10^19.