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

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. One approach to GUP is called linear-quadratic GUP (LQGUP) which satisfies both the minimum measurable length and the maximum measurable momentum, resulting to an infinitesimal phase space volume proportional to the first-order momentum $(1-\alpha p{)}^{-4}{d}^{3}x{d}^{3}p$, where $\alpha$ is the still-unestablished GUP parameter. In this study, we explore the mass-radius relations of white dwarfs whose equation of state has been modified by LQGUP, and provide them with radial perturbations to investigate the dynamical instability arising from the oscillations. We find from the mass-radius relations that the main effect of LQGUP is to worsen the gravitational collapse by decreasing the mass of the relatively massive white dwarfs (including their limiting mass, while increasing their limiting radius). This effect gets more prominent with larger values of $\alpha$. We then compare the results with available observational data. To further investigate the impact of the GUP parameter, a dynamical instability analysis of the white dwarf was conducted, and we find that instability sets in for all values of $\alpha$. With increasing $\alpha$, we also find that the central density at which instability occurs decreases, resulting to a lower maximum mass. This is in contrast to quadratic GUP, where instability only sets in below a critical value of the quadratic GUP parameter.

References in corpus (36)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• On the Origin of Gravity and the Laws of Newton
• Lorentz invariance with an invariant energy scale
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• White Dwarf Mass Distribution in the SDSS
• Generalized Uncertainty Principle: Approaches and Applications
• Quantum Uncertainty in Doubly Special Relativity
• Gravitational tests of the Generalized Uncertainty Principle
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• GUP parameter from quantum corrections to the Newtonian potential
• Review on Generalized Uncertainty Principle
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Neutron Stars for Undergraduates
• Measurements of Physical Parameters of White Dwarfs: A Test of the Mass-Radius Relation
• The Lowest Mass White Dwarf
• Confronting nuclear equation of state in the presence of dark matter using GW170817 observation in relativistic mean field theory approach
• White dwarfs and revelations
• GUP parameter and black hole temperature
• The deformation parameter of the generalized uncertainty principle
• Quantum gravity effects on statistics and compact star configurations
• Linear and Quadratic GUP, Liouville Theorem, Cosmological Constant, and Brick Wall Entropy
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Quantum gravity effects on compact star cores
• Effects of the Generalized Uncertainty Principle on Compact Stars
• Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs
• A Critique on Some Aspects of GUP Effective Metric
• Equilibrium structure of white dwarfs at finite temperatures
• Effect of minimal length uncertainty on the mass-radius relation of white dwarfs
• Existence of Chandrasekhar's limit in GUP white dwarfs
• On the Chandrasekhar Limit in Generalized Uncertainty Principles
• Minimal Length, Nuclear Matter, and Neutron Stars
• Stability of Neutron Stars with Dark Matter Core Using Three Crustal Types and the Impact on Mass-Radius Relations
• Virtual Black Holes from Generalized Uncertainty Principle and Proton Decay
• Prospect of Chandrasekhar's limit against modified dispersion relation

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• Linear-Quadratic GUP and Thermodynamic Dimensional Reduction
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