Minimally deformed wormhole solutions with holographic dark energy and mixed energy density in dRGT gravity

Abstract

This study explores static, spherically symmetric wormhole solutions within the framework of massive gravity (dRGT) de Rham–Gabadadze–Tolley (dRGT) for the first time, incorporating mixed-energy density and holographic dark energy (DE) density profiles using the Minimal Geometric Deformation (MGD) method proposed by Ovalle (2017). Using unique density profiles, the corresponding shape functions are calculated. The key characteristics of wormholes, including flaring-out condition and asymptotical flatness, are examined in depth. Through the MGD approach, this study constructs wormhole solutions, with the decoupling parameter $\gamma$ serving as a key factor influencing their geometry and energy constraints. The embedded diagrams illustrate the upper and lower universes, which are influenced by the effects of newly determined shape functions. In addition, the volume integral quantifier ($\mathrm{VIQ}$) is evaluated, shedding light on the exotic matter required near the wormhole throat. The stability of the wormhole solution is confirmed by satisfying equilibrium criteria through the balancing of different forces. Both models suggest that real-world wormhole solutions are feasible due to the increasing active gravitational mass ($\mathrm{AGM}$). Through a detailed analysis of shape functions, the study addresses how thin-shell wormhole stability is influenced by mass, geometric structure, and decoupling parameter, offering practical insights into constructing stable configurations in theoretical models.