  Generalized uncertainty relation that carries the imprint of quantum gravity
introduces a minimal length scale into the description of space-time. It
effectively changes the invariant measure of the phase space through a factor
$(1+\beta \mathbf{p}^2)^{-3}$ so that the equation of state for an electron gas
undergoes a significant modification from the ideal case. It has been shown in
the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to
exist when the modified equation of state due to the generalized uncertainty is
taken into account. To assess the situation in a more complete fashion, we
analyze in detail the mass-radius relation of Newtonian white dwarfs whose
hydrostatic equilibria are governed by the equation of state of the degenerate
relativistic electron gas subjected to the generalized uncertainty principle.
As the constraint of minimal length imposes a severe restriction on the
availability of high momentum states, it is speculated that the central Fermi
momentum cannot have values arbitrarily higher than $p_{\rm
max}\sim\beta^{-1/2}$. When this restriction is imposed, it is found that the
system approaches limiting mass values higher than the Chandrasekhar mass upon
decreasing the parameter $\beta$ to a value given by a legitimate upper bound.
Instead, when the more realistic restriction due to inverse $\beta$-decay is
considered, it is found that the mass and radius approach the values close to
$1.45$ M$_{\odot}$ and $600$ km near the legitimate upper bound for the
parameter $\beta$. On the other hand, when $\beta$ is decreased sufficiently
from the legitimate upper bound, the mass and radius are found to be
approximately $1.46$ M$_{\odot}$ and $650$ km near the neutronization
threshold.
