Unraveling the mysteries of wormhole formation in Rastall-Rainbow gravity: A comprehensive study using the embedding approach

TL;DR

This study explores static, spherically symmetric wormhole solutions within Rastall-Rainbow gravity, revealing conditions for traversability, energy condition violations, and stability, while highlighting the influence of model parameters on wormhole characteristics.

Contribution

It provides an analytical framework for wormhole solutions in Rastall-Rainbow gravity using the embedding approach and examines their stability and energy conditions.

Findings

Traversable wormholes violate null and weak energy conditions.

Wormhole stability depends on adiabatic sound velocity analysis.

Model parameters significantly influence wormhole properties.

Abstract

The present work looks for the possible existence of static and spherically symmetric wormhole geometries in Rastall-Rainbow gravity. Since, the Rastall-Rainbow gravity model has been constructed with the combination of Rastall theory and the gravity's rainbow formalism. Taking advantage of the Karmarkar condition for embedding class one metrics, we solve the modified field equations analytically that describe wormholes for specific choice of redshift function. For specific parameter ranges, the solution represents a traversable wormhole that exhibits the violation of null energy condition and consequently the weak energy condition also. Furthermore, we focus on the wormhole stability via adiabatic sound velocity analysis. This model establishes a strong connection between two model parameters, namely, the Rastall parameters and the Rainbow functions, and how it affects the wormhole solution.