Complexity factor for a static self-gravitating sphere in Rastall-Rainbow gravity

TL;DR

This paper extends the concept of complexity factor to static spherically symmetric fluid distributions within Rastall-Rainbow gravity, revealing its geometric significance and applicability to star modeling.

Contribution

It generalizes Herrera's complexity factor to Rastall-Rainbow gravity, linking it to the deviation in active gravitational mass and demonstrating its use in star models.

Findings

Complexity factor appears in the Riemann tensor splitting.

Vanishing complexity condition matches that in general relativity.

Results reduce to GR in the low-energy limit.

Abstract

We generalized Herrera's definition of complexity factor for static spherically symmetric fluid distributions to Rastall-Rainbow theory of gravity. For this purpose, an energy-dependent equation of motion is employed in accordance with the principle of gravity's rainbow. It is found that the complexity factor appears in the orthogonal splitting of the Riemann curvature tensor, and measures the deviation of the value of the active gravitational mass from the simplest system under the combined corrections of Rastall and rainbow. In the low-energy limit, all the results we have obtained reduce to the counterparts of general relativity when the non-conserved parameter is taken to be one. We also demonstrate how to build an anisotropic or isotropic star model using complexity approach. In particular, the vanishing complexity factor condition in Rastall-Rainbow gravity is exactly the same as that derived in general relativity. This fact may imply a deeper geometric foundation for the complexity factor.