Implications of the generalized uncertainty principle on the Walecka model equation of state and neutron star structure

Abstract

We explore the implications of the generalized uncertainty principle (GUP) on the nuclear equation of state (EoS) and on the structure of neutron stars. Two approaches of GUP are used: the quadratic GUP approach, satisfying minimal length and the linear GUP approach, satisfying both minimal length and maximal momentum. The resulting invariant phase space volumes from these GUP approaches are applied to the [Formula: see text]-[Formula: see text] or Walecka model, serving as a starting point for neutron matter in the relativistic mean field theory. We find that linear GUP increases the range of energy densities corresponding to instabilities in the [Formula: see text]-[Formula: see text] EoS, while quadratic GUP decreases it. A stable EoS was constructed from the GUP-modified EoS via Maxwell construction, and this was fed into the Tolman–Oppenheimer–Volkoff equations and the mass–radius relation of neutron stars was obtained. We observe linear GUP to decrease both the maximum mass and limiting radius of the neutron star, while shifting the whole mass–radius relation to the low-radius regime. Meanwhile, quadratic GUP increases the maximum mass and limiting radius, and the mass-radius relation is shifted to the high-radius regime. The effects that are observed for both GUP modifications in the EoS and mass–radius relations get more prominent as we increase the values of the still unknown GUP parameters.

On the Chandrasekhar Limit in Generalized Uncertainty Principles

“…Therefore, an assessment of the uncertainty relation proposed in [14] with respect to these astrophysical requirements is in order. We refer the reader also to [28][29][30][31][32] for some further investigations of the properties of stellar configurations in gravitational equilibrium in other-than-Heisenberg models.…”

“…The material of which white dwarfs are made can be approximated as a degenerate gas of electrons (fermions) at temperature T ∼ 0. The uncertainty principle affects the properties of such a gas, like the density of particles, its pressure and total energy, which may have further consequences on the condition of gravitational equilibrium governing the existence of the star [19,[28][29][30]. Taking into account the correction to the phase space volume [45, Eq.…”

“…We should also appreciate some drastic differences in the behavior at high Fermi momentum ξ → ∞ of the degenerate electron gas in the framework of the GUP* as compared to that of the GUP explored in ( [19,[28][29][30]): (i) the number density no longer approaches a constant but is rather diverging as it would be predicted by the usual Heisenberg's Uncertainty principle; (ii) the same would be for the internal kinetic energy; (iii) the pressure is diverging faster compared to the usual GUP approach; (iv) for the relativistic adiabatic index we obtain γ → 5/4 ≈ 1.25 for ξ → ∞, which is in better agreement with the result of an ideal gas γ ideal = 4/3 ≈ 1.333 than the result of γ ≈ π β3 16 found in the context of GUP. More quantitatively, we should note that the highest power term in ξ may actually be diminished by some factor in β, and thus the asymptotic expression to consider are…”

Minimal length, nuclear matter, and neutron stars

“…On the other hand, as far as we know that the impacts of GUP on NS properties were only discussed in Ref. [37]. The authors use the linear RMF (Walecka) model and general relativity (GR) to describe EoS and gravity, respectively.…”