Research Paper: The Effect of the Generalized Uncertainty Principle with Maximum Length on the Size of White Dwarfs

Abstract

The challenge in developing a theory of quantum gravity stems from the fundamentally different ways the two theories describe physical systems. Quantum mechanics operates on discrete, probabilistic principles, while general relativity is a continuous, deterministic theory. The generalized uncertainty principle is a modified version of Heisenberg's uncertainty principle that applies quantum gravitational corrections to systems with strong gravity. As a clear example of these systems, white dwarfs can be mentioned. In white dwarfs, the gravitational pressure provides the necessary support against gravitational collapse, however, the generalized uncertainty principle has been shown to negate the Chandrasekhar limit in the presence of a minimum length, allowing white dwarfs to grow to any size, even infinitely large, which is in contradiction with physical astrophysical observations. This paper modifies the relationship between degeneracy pressure and density in white dwarfs using an alternative form of the uncertainty principle that incorporates a maximum length. We demonstrate that this new formalism recovers the Chandrasekhar limit and resolves the discrepancy between theory and observation.

Keywords

• generalized uncertainty principle
• quantum gravity
• chandrasekhar limit
• white dwarfs
• maximum length