Effect of GUP on the Kepler problem and a variable minimal length
arXiv:1411.0241 · doi:10.1139/cjp-2013-0354
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
arXiv comment8 pages
References in corpus (12)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum gravity and minimum length
- The Generalized Uncertainty Principle and Black Hole Remnants
- Universality of Quantum Gravity Corrections
- Discreteness of Space from the Generalized Uncertainty Principle
- Quantum Groups, Gravity, and the Generalized Uncertainty Principle
- Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
- Black Hole Remnants and Dark Matter
- On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
- A class of GUP solutions in deformed quantum mechanics
- Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry
- Planck Length and Cosmology
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