Minimal Length, Nuclear Matter, and Neutron Stars

In this paper, we employ one variant of the Generalized Uncertainty Principle (GUP) model, i.e., the Kempf-Mangano-Mann (KMM) model, and discuss the impact of GUP on the EoS of nuclear and neutron star matter based on the Relativistic Mean Field (RMF) model. We input the result in the Serrano-Li\v{s}ka (SL) gravity theory to discuss the corresponding Neutron Star (NS) properties. We have shown that the upper bound for the GUP parameter from nuclear matter properties is $\beta \leq 2\times10^{-7}$ MeV$^{-2}$. If we used this $\beta$ upper bound to calculate NS matter, and considering SL parameter $\tilde{c}$ as an independent parameter, we have found that the upper bound for the SL parameter, which modifies the Einstein field equation, is $\tilde{c} \leq 10^7$ m$^2$. This beta upper bound is determined by considering the anisotropy magnitude smaller than the pressure magnitude. By employing $\beta =2\times10^{-7}$ MeV$^{-2}$ and $\tilde{c} = 10^7$ m$^2$, we obtain the mass-radius relation that satisfies NICER data for both PSR J0740+6620 (whose mass is $\sim 2.1M_\odot$) and PSR J0030+0451 ($M\sim 1.4M_\odot$). Our GUP parameter upper bound perfectly matches the constraint from $^{87}$Rb cold-atom-recoil experiment. If we consider that the same strength from the additional logarithmic term in the entropy from both GUP and SL model are dependent, for $\beta < 2\times10^{-7}$ MeV$^{-2}$, it is clear that SL parameter lower bound is $\tilde{c} > -16\times 10^{-34}$ m$^2$. The magnitude of this bound is $10^{-40}$ smaller than the upper bound magnitude of SL parameter considering as independent parameter i.e., $\tilde{c} \leq 10^7$ m$^2$.