Modified structure equations and mass–radius relations of white dwarfs arising from the linear generalized uncertainty principle

Abstract

The generalized uncertainty principle (GUP) is a common feature among several approaches related to quantum gravity. An approach to GUP was recently developed that contains both linear and quadratic terms of momenta, from which an infinitesimal phase space volume was derived up to the linear term of momenta. We studied the effects of this linear GUP approach on the structure equations and mass–radius relation of zero-temperature white dwarfs. We formulated a linear GUP-modified Chandrasekhar equation of state (EoS) by deriving exact forms of the thermodynamic properties of ideal Fermi gases. This was then used to obtain the analytical form of the modified Newtonian structure equations for the white dwarfs. By imposing a constraint on the momenta of the particles in the white dwarf due to linear GUP, the structure equations were solved and the modified mass–radius relation of the white dwarfs were obtained. This was then extended in the context of general relativity (GR), which, like linear GUP, affects white dwarfs significantly in the high-mass regime. We found that linear GUP displays a similar overall effect as in GR — linear GUP supports gravitational collapse of the white dwarf, by decreasing its limiting (maximum) mass and increasing its corresponding limiting (minimum radius). We also found that GUP effects become evident only at large values of the GUP parameter, but these values are still within the estimated bounds. This effect gets more prominent as we increase the as-of-yet unestablished value of the parameter.

On the Chandrasekhar Limit in Generalized Uncertainty Principles

“…Therefore, an assessment of the uncertainty relation proposed in [14] with respect to these astrophysical requirements is in order. We refer the reader also to [28][29][30][31][32] for some further investigations of the properties of stellar configurations in gravitational equilibrium in other-than-Heisenberg models.…”

“…The material of which white dwarfs are made can be approximated as a degenerate gas of electrons (fermions) at temperature T ∼ 0. The uncertainty principle affects the properties of such a gas, like the density of particles, its pressure and total energy, which may have further consequences on the condition of gravitational equilibrium governing the existence of the star [19,[28][29][30]. Taking into account the correction to the phase space volume [45, Eq.…”

“…We should also appreciate some drastic differences in the behavior at high Fermi momentum ξ → ∞ of the degenerate electron gas in the framework of the GUP* as compared to that of the GUP explored in ( [19,[28][29][30]): (i) the number density no longer approaches a constant but is rather diverging as it would be predicted by the usual Heisenberg's Uncertainty principle; (ii) the same would be for the internal kinetic energy; (iii) the pressure is diverging faster compared to the usual GUP approach; (iv) for the relativistic adiabatic index we obtain γ → 5/4 ≈ 1.25 for ξ → ∞, which is in better agreement with the result of an ideal gas γ ideal = 4/3 ≈ 1.333 than the result of γ ≈ π β3 16 found in the context of GUP. More quantitatively, we should note that the highest power term in ξ may actually be diminished by some factor in β, and thus the asymptotic expression to consider are…”

A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound

“…Similar to the GUP featuring linear p-modifications [8,13,[91][92][93][94], our approach incorporates a deformed phase space measure characterized by the deformation parameter γ. In the context of GUP, this deformation is determined through the application of the Liouville theorem [92].…”

Bose and Fermi Gases in Metric-Affine Gravity and Linear Generalized Uncertainty Principle

“…As we can see from (11), the deformation in the phase space introduced here is parameterized by σ. Hence, the procedure described in this work can be paralleled to the GUP theories containing linear corrections in p [53][54][55][56][57][58]. In the context of the GUP, the deformation is derived through the utilization of the Liouville theorem [59].…”