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High Energy Physics - Phenomenology, hep-ph, Astrophysics, Solar and Stellar Astrophysics, astro-ph.SR,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We study the mass-radius relations of finite temperature white dwarfs
modified by the quadratic generalized uncertainty principle (QGUP), a
prediction that arises from quantum gravity phenomenology. This QGUP approach
extends the Heisenberg uncertainty principle by a quadratic term in momenta,
which then modifies the phase space volume in the Chandrasekhar equation of
state (EoS). This EoS was first calculated by treating the GUP parameter
$\beta$ as perturbative. This perturbative EoS exhibits the expected thermal
deviation for low pressures, while showing conflicting behaviors in the high
pressure regime dependent on the sign of the $j$th order of approximation,
$(\mathcal{O}(\beta^j))$. To explore the effects of QGUP further, we proceed
with a full numerical simulation, and showed that in general, finite
temperatures cause the EoS at low pressures to soften, while QGUP 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.
