Effect of GUP on the Kepler problem and a variable minimal length

TL;DR

This paper explores how the Generalized Uncertainty Principle (GUP), which predicts a minimal measurable length, affects planetary orbits and stability in spacetime, linking it to the cosmological constant and its potential variability.

Contribution

It introduces a GUP model preserving rotational symmetry and analyzes its impact on the Kepler problem, perihelion shift, and orbit stability, connecting minimal length to the cosmological constant.

Findings

Derived a relation between minimal length and cosmological constant.

Showed that a variable cosmological constant implies a variable minimal length.

Analyzed the impact of GUP on the stability of circular orbits.

Abstract

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg Uncertainty Principle near the Plank scale, known as the Generalized Uncertainty Principle (GUP). Here we study the effects of GUP which preserves the rotational symmetry of the spacetime, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild-de Sitter spacetime with the resulted value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the spacetime. Now, if the cosmological constant varies with time, we have a variable minimal length in the spacetime. Finally, we investigate the effects of GUP on the stability of circular orbits