Existence of Chandrasekhar’s limit in generalized uncertainty white dwarfs

Abstract

The existence of Chandrasekhar’s limit has played various decisive roles in astronomical observations for many decades. However, various recent theoretical investigations suggest that gravitational collapse of white dwarfs is withheld for arbitrarily high masses beyond Chandrasekhar’s limit if the equation of state incorporates the effect of quantum gravity via the generalized uncertainty principle. There have been a few attempts to restore the Chandrasekhar limit but they are found to be inadequate. In this paper, we rigorously resolve this problem by analysing the dynamical instability in general relativity. We confirm the existence of Chandrasekhar’s limit as well as stable mass–radius curves that behave consistently with astronomical observations. Moreover, this stability analysis suggests gravitational collapse beyond the Chandrasekhar limit signifying the possibility of compact objects denser than white dwarfs.

On the Chandrasekhar Limit in Generalized Uncertainty Principles

“…Although this result has resolved the tension between astrophysical observations and some GUP models, it may not fully reflect Chandrasekhar's way of thinking who emphasized that his mass limit actually arises when the size of the white dwarf is vanishing 1 [21]. In this paper, we will show that following the same method of [19], but adopting the uncertainty principle called GUP* formulated in [14], it is possible to re-obtain the Chandrasekhar mass consistently with his point of view.…”

“…It is clear that meaningful extensions of the Heisenberg principle should not only tame open tensions but also being consistent with all the previously well established physics. For example, when describing the matter content of white dwarfs and neutron stars adopting the GUP, (re-)obtaining the maximum value for the stellar mass has required some not-so-trivial thinking [16][17][18][19]. This is a crucial test that newly formulated theories need to pass because a maximum value for such masses has been theoretically predicted by various authors like Chandrasekhar [20,21], Landau [22], Stoner [23], Tolman-Oppenheimer-Volkoff [24,25] and confirmed observationally [26,27].…”

“…In fact it was already suggested in [16] that the GUP-corrected Tolman-Oppenheimer-Volkoff (TOV) equation would be required to fully model the stars; though in that work it was instead suggested as a possible solution that perhaps the GUP parameter is negative. Subsequently, in [19,Sect.3.1.2] it was explained how to obtain the maximum value for the mass of a white dwarf in the high-momentum limit by implementing the equation of state of a degenerate electron gas, which is sensitive to the GUP corrections, into the Tolman-Oppenheimer-Volkoff equations; the procedure worked as follows: the mass-radius relation was obtained, the maximum radius of the configuration was estimated and then used in that equation to get the maximum value of the mass. Although this result has resolved the tension between astrophysical observations and some GUP models, it may not fully reflect Chandrasekhar's way of thinking who emphasized that his mass limit actually arises when the size of the white dwarf is vanishing 1 [21].…”

“…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…”