Designing Wormholes in Novel Power-Law $f(R)$: A Mathematical approach with a linear equation of state

TL;DR

This paper constructs and analyzes various wormhole solutions within $f(R)$ gravity, exploring their physical properties, energy conditions, and astrophysical signatures like photon spheres, with implications for cosmology and modified gravity theories.

Contribution

It introduces four novel $f(R)$ wormhole models with diverse geometries and energy conditions, and examines their cosmological viability and astrophysical features.

Findings

Some wormholes satisfy null energy conditions but are supported by ghost $f(R)$ models.

One wormhole is asymptotically flat with zero tidal force.

Photon sphere properties are consistent with Einstein gravity, unaffected by $f(R)$ modifications.

Abstract

We consider the inhomogeneous Morris-Thorne wormhole metric with matter tensors characterised by a novel linear equation of state in $f(R)$ gravity. Using the Einstein's field equations in metric $f(R)$ gravity we model solutions for both wormhole as well as $f(R)$ gravity. We obtain four different wormhole models, two wormholes are characterised by solid angle deficit, three are not asymptotically extendible, while one is asymptotically flat with zero tidal force. These are supported by four different power law $f(R)$ models. The parameter space of the models can support both null energy conditions (NEC) satisfying as well as violating wormhole. In case of NEC satisfying matter, the associated $f(R)$ is ghost. The $f(R)$ models obtained have been independently substantiated for cosmological feasibility and valid parameter space was obtained corresponding to cosmologically viable $f(R)$. Suitable scalar-tensor representation of the corresponding $f(R)$ models have been presented using the correspondence of $f(R)$ gravity with Brans-Dicke (BD) theory of gravity. The robustness of the wormhole solutions were further analysed with the BD scalar fields in the hybrid metric-Palatini gravity, which showed excellent results. Lastly as an independent astrophysical probe for the wormhole we have obtained the location of their photon spheres and have connected them with the Herrera Complexity factor in $f(R).$ Our results show that the relation between the complexity factor and existence of photon spheres remains fundamentally unaltered in $f(R)$ as compared to Einstein's gravity.