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Abstract

A modification to the Heisenberg uncertainty principle is called the
generalized uncertainty principle (GUP), which emerged due to the introduction
of a minimum measurable length, common among phenomenological approaches to
quantum gravity. An approach to GUP called linear GUP (LGUP) has recently been
developed that satisfies both the minimum measurable length and the maximum
measurable momentum, resulting to a phase space volume proportional to the
first-order momentum $(1 - \alpha p)^{-4} d^3x d^3p$, where $\alpha$ is the
still-unestablished GUP parameter. In this study, we explore the mass-radius
relations of LGUP-modified white dwarfs, and provide them with radial
perturbations to investigate the dynamical instability arising from the
oscillations. We find from the mass-radius relations that LGUP results to a
white dwarf with a lower maximum mass, and this effect gets more apparent with
larger the values of $\alpha$. We also observe that the mass of the white dwarf
corresponding to the vanishing of the square of the fundamental frequency
$\omega_0$ is the maximum mass the white dwarf can have in the mass-radius
relations. The dynamical instability analysis also shows that instability sets
in for all values of the GUP parameters $\alpha$, and at lower central
densities $\rho_c$ (corresponding to lower maximum masses) for increasing
$\alpha$, which verifies the results obtained from the mass-radius relations
plots. Finally, we note that the mass limit is preserved for LGUP-modified
white dwarfs, indicating that LGUP supports gravitational collapse of the
compact object.