Noncommutativity of four-dimensional axisymmetric spacetime in polar coordinate

TL;DR

This paper explores how noncommutative geometry, defined via the generalized Moyal product, affects axisymmetric spacetimes like Kerr, showing modifications to the stationary limit surface and suggesting a softened gravitational interaction.

Contribution

It demonstrates consistent noncommutativity in axisymmetric spacetimes using the generalized Moyal product, extending the application beyond Cartesian coordinates.

Findings

Noncommutativity modifies the shape of the stationary limit surface.

Noncommutative effects imply an effective softening of gravity.

Consistent noncommutativity can be achieved in polar coordinates.

Abstract

It is shown that in the noncommutative spacetime defined by the generalized Moyal product, consistent noncommutativity can be obtained independent of the coordinate system such as Cartesian or polar one. In addition, based on the fact that the generalized Moyal product can be applied to arbitrary spacetime with non-trivial curvature, the effect of noncommutativity in the axisymmetric spacetime with central mass is investigated. The results demonstrate how the noncommutativity of spacetime modify the shape of the stationary limit surface in the noncommutative Kerr spacetime, which implies that the gravitational interaction seems to be effectively softened.