On the Stability of Planetary Circular Orbits in Noncommutative Spaces

TL;DR

This paper explores how space noncommutativity influences the stability and radius of circular orbits in central force and Schwarzschild spacetimes, revealing that noncommutativity enlarges stable orbit radii and alters stability conditions.

Contribution

It introduces a noncommutative effective potential with an angular momentum dependent term, analyzing its impact on orbital stability in both classical and relativistic contexts.

Findings

Stable orbit radius increases in noncommutative space.

Noncommutativity modifies stability conditions for large angular momentum.

Effective potential gains an angular momentum dependent correction.

Abstract

We investigate the effects of space noncommutativity and the generalized uncertainty principle on the stability of circular orbits of particles in both a central force potential and Schwarzschild spacetime. We find noncommutative form of the effective potential which up to first order of noncommutativity parameter contains an angular momentum dependent extra term. This angular momentum dependent extra term affects the stability of circular orbits in such a way that the radius of a stable circular orbit in noncommutative space is larger than its commutative counterpart. In the case of large angular momentum, the condition for stability of circular orbits in noncommutative space differs considerably from commutative case.