| Popis: |
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. |
