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#### Radial Oscillations and Dynamical Instability Analysis for Linear GUP-modified White Dwarfs

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##### Citation

Bernaldez, J. P. R., Abac, A., & Otadoy, R. E. S. (in preparation). Radial Oscillations and Dynamical Instability Analysis for Linear GUP-modified White Dwarfs.

Cite as: https://hdl.handle.net/21.11116/0000-000B-6648-2

##### 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.

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.