On the Chandrasekhar Limit in Generalized Uncertainty Principles

Abstract

The Chandrasekhar limit for white dwarfs has been confirmed by many astrophysical observations. However, how to obtain it theoretically in models which rely on other-than-Heisenberg's Uncertainty principles, which are predicted by some quantum gravity theories, is not a trivial task. In this manuscript, we will derive the Chandrasekhar mass assuming an uncertainty relation proposed in the framework of Doubly Special Relativity, exhibiting both a minimal length and a maximum momentum. We found that the Chandrasekhar mass arises when the size of the star becomes arbitrarily small, the same behavior as in the original Chandrasekhar's derivation, but not when the more popular Generalized Uncertainty Principle is assumed. We will argue that this is related to the difference in the classical limit of these two different generalized uncertainty principles. The role of a maximum momentum in guaranteeing the stability of the configuration is also analyzed.

Removing the divergence of Chandrasekhar limit caused by generalized uncertainty principle

“…We have shown two independent solutions to restore the mass limit of white dwarf from two scenarios including positive and negative parameters. For the case of positive parameter, we can see the divergence can be removed by a maximal momentum, agreeing with the suggestions given in [28,40]. But for the case of negative parameter, there is still a lack of physical meaning to explain why the negative sign can restore the mass limit.…”

“…In this section, we explore another solution for the case of positive parameter from an improved generalized uncertainty principle, and the difference from the former is that a definite limit for momentum is obtained. Besides, a similar investigation is shown in [40], which gets a maximum momentum from a higher order generalized uncertainty principle. In the next section, we will see that the mass limit can also be restored by a negative sign of parameter.…”

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

“…The GUP models introduce modifications to equations of state and microscopic variables, stemming from the interplay between special relativity and gravity. This proposition incorporates a dispersion relation involving energy, mass, and momentum within Heisenberg's Uncertainty Principle, incorporating constants such as the speed of light and the gravitational constant [33,[37][38][39][40][41].…”

Fermi gas and modified gravity

“…One also alters thermodynamics quantities and EoS's when dealing with (pseudo-)scalar fields, for instance, axions [67]. Another manifestation of special relativity and gravity appearing as the corrections to the EoS's and other mi-croscopic variables is provided by the Generalized Uncertainty Principles which is, roughly speaking, a proposal of how the dispersion relation between energy, mass and momentum represented by the speed of light c, and gravity, given by the Newtonian constant G, should be present in Heisenberg's Uncertainty principle [34,[68][69][70][71][72].…”