Dark Energy Stars in Rastall-Rainbow Gravity: Structure, Stability and Observational Constraints

TL;DR

This paper explores the structure and stability of dark energy stars within Rastall-Rainbow gravity, demonstrating that this modified gravity framework can produce stable, observationally consistent stellar configurations with distinct structural features.

Contribution

It introduces a novel analysis of dark energy stars in Rastall-Rainbow gravity, deriving modified equations, and assessing observational viability with high-mass pulsars and gravitational wave data.

Findings

R-R gravity influences maximum mass and radius of stars.

Stable configurations are achievable within certain parameter ranges.

Deviations from general relativity affect star properties systematically.

Abstract

In this work, we investigate static configurations of dark energy stars within the framework of Rastall-Rainbow (R-R) gravity, which combines an energy-dependent deformation of spacetime with a nonminimal coupling between matter and geometry. We begin by deriving the modified field equations corresponding to R-R gravity and subsequently reformulate the stellar structure equations to describe hydrostatic equilibrium. The generalized Tolman-Oppenheimer-Volkoff (TOV) equations are then solved numerically by adopting the modified Chaplygin equation of state to model the interior matter distribution. The R-R parameters, along with fluid constants, are shown to influence the maximum mass, radii, and stiffness of the star sequences compared to the baseline set by general relativity. We apply observational benchmarks from high-mass pulsars and binary-merger events (e.g., GW170817 and GW190814) to appraise viability within the explored parameter space. The results collectively suggest that stable, causal configurations arise from physically meaningful parameter selections, with deviations from general relativity leading to systematic changes in structural characteristics while adhering to theoretical limits. These findings illustrate that Rastall-Rainbow gravity can support stable, observationally consistent dark energy stars, providing verifiable signatures in strong gravitational fields.