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 will show how to re-obtain an asymptotically vanishing radius for the star in the limiting subcase of the Heisenberg uncertainty principle: this is 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, enlightening that the modified uncertainty parameter considered here behaves like a finite temperature. The role of a maximum momentum in guaranteeing the stability of the configuration, and in providing a finite pressure for the degenerate electrons' gas, is also analyzed.