Removing the divergence of Chandrasekhar limit caused by generalized uncertainty principle

Abstract

The usual generalized uncertainty principle will lead to a divergent mass limit of white dwarf, and this divergence should be prevented for both scenarios including positive and negative parameters of generalized uncertainty principle. Although it has been shown that negative parameter can directly restore the mass limit, the underlying reason is not given to explain why the negative sign appears under the condition of white dwarf. In order to solve this problem, we derive a field-dependent parameter expression whose sign can change depending on the species of spin fields. Besides, we find that the actual physical effect of the negative sign is aimed at limiting the exorbitant uncertainty of momentum.

New generalized uncertainty principle with parameter adaptability for the minimum length

“…For eq. (1.1), a similar parameter expression is shown in [12], and the only difference from eq. (3.2) is that the coefficient 1/(360π) is rewritten as 2/(45π), which does not affect the changing process of the parameter sign.…”

“…It means that NGUP not only has a good parameter adaptability for the minimum length but also reflects the maximum momentum supported by most high-order generalized uncertainty principles [20,21]. In addition, only KMM provides the maximum momentum when the parameter is negative, which can restore the Chandrasekhar limit corrected by the generalized uncertainty principle [12]. It seems that the maximum momentum should also be maintained under different parameter signs, just like the minimum length.…”

“…Although the parameter α is not explicitly defined, it is often regarded as a positive value to keep the minimum length (∆x) min = √ αL p existing. In recent years, there have been many papers suggesting the parameter of the generalized uncertainty principle should be negative rather than positive in some specific scenarios such as: a metric to reproduce the Hawking temperature deformed by the generalized uncertainty principle [7], an uncertainty relation from a crystal-like universe [8], the sparsity of Hawking radiation affected by rainbow gravity [9], the Magueijo and Smolin formulation of doubly special relativity [10], and a method to restore the Chandrasekhar limit modified by the generalized uncertainty principle [11,12]. Therefore, different quantum gravitational models might lead to different parameter signs (positive or negative), and the parameter sign should be treated as a changeable object.…”