Eur. Phys. J. C (2022) 82: 884
https://doi.org/10.1140/epjc/s10052-022-10849-1

Regular Article - Theoretical Physics

Minimal length, nuclear matter, and neutron stars

¹ Department of General Education, Faculty of Art and Sciences, Sampoerna University, 12780, Jakarta, Indonesia
² IoT and Physics Lab, Sampoerna University, 12780, Jakarta, Indonesia
³ Prodi Sains Atmosfer dan Keplanetan, Jurusan Sains Institut Teknologi Sumatera, 35365, Lampung Selatan, Indonesia
⁴ Observatorium Astronomi ITERA Lampung, Institut Teknologi Sumatera, 35365, Lampung Selatan, Indonesia
⁵ Theoretical High Energy Physics Research Division, Institut Teknologi Bandung, Jl. Ganesha 10, 40132, Bandung, Indonesia
⁶ Departemen Fisika FMIPA Universitas Indonesia, Kampus UI, 16424, Depok, Indonesia

^a ilham.prasetyo@sampoernauniversity.ac.id

Received: 5 August 2022
Accepted: 25 September 2022
Published online: 7 October 2022

Abstract

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–Liška (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 $\beta \le 2\times {10}^{-7}$ 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 $\tilde{c}\le {10}^7$ m${}^2$. This beta upper bound is determined by considering the anisotropy magnitude smaller than the pressure magnitude. By employing $\beta =2\times {10}^{-7}$ 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 $\beta <2\times {10}^{-7}$ 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., $\tilde{c}\le {10}^7$ m${}^2$.