The generalized uncertainty principle (GUP) is a common feature among several approaches related to quantum gravity. An approach to GUP was recently developed that contains both linear and quadratic terms of momenta, from which an infinitesimal phase space volume was derived up to the linear term of momenta. We studied the effects of this linear GUP approach on the structure equations and mass–radius relation of zero-temperature white dwarfs. We formulated a linear GUP-modified Chandrasekhar equation of state (EoS) by deriving exact forms of the thermodynamic properties of ideal Fermi gases. This was then used to obtain the analytical form of the modified Newtonian structure equations for the white dwarfs. By imposing a constraint on the momenta of the particles in the white dwarf due to linear GUP, the structure equations were solved and the modified mass–radius relation of the white dwarfs were obtained. This was then extended in the context of general relativity (GR), which, like linear GUP, affects white dwarfs significantly in the high-mass regime. We found that linear GUP displays a similar overall effect as in GR — linear GUP supports gravitational collapse of the white dwarf, by decreasing its limiting (maximum) mass and increasing its corresponding limiting (minimum radius). We also found that GUP effects become evident only at large values of the GUP parameter, but these values are still within the estimated bounds. This effect gets more prominent as we increase the as-of-yet unestablished value of the parameter.

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.

In quantum gravity phenomenology, the effect of the generalized uncertainty principle (GUP) on white dwarf structure has been given much attention in recent literature. However, these studies assume a zero temperature equation of state (EoS), excluding young white dwarfs whose initial temperatures are substantially high. To that cause, this paper calculates the Chandrasekhar EoS and resulting mass-radius relations of finite temperature white dwarfs modified by the quadratic GUP, an approach that extends Heisenberg’s uncertainty principle by a quadratic term in momenta. The EoS was first approximated by treating the quadratic GUP parameter as perturbative, causing the EoS to exhibit expected thermal deviations at low pressures, and conflicting behaviors at high pressures, depending on the order of approximation. We then proceeded with a full numerical simulation of the modified EoS, and showed that in general, finite temperatures cause the EoS at low pressures to soften, while the quadratic GUP stiffens the EoS at high pressures. This modified EoS was then applied to the Tolman–Oppenheimer–Volkoff equations and its classical approximation to obtain the modified mass-radius relations for general relativistic and Newtonian white dwarfs. The relations for both cases were found to exhibit the expected thermal deviations at small masses, where low-mass white dwarfs are shifted to the high-mass regime at large radii, while high-mass white dwarfs acquire larger masses, beyond the Chandrasekhar limit. Additionally, we find that for sufficiently large values of the GUP parameter and temperature, we obtain mass-radius relations that are completely removed from the ideal case, as high-mass deviations due to GUP and low-mass deviations due to temperature are no longer mutually exclusive.