## “Wormhole Configurations in $kappa(mathcal{R},mathcal{T})

arXiv:2403.19733v1 Announce Type: new

Abstract: We present an exhaustive study of wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state $p(r)=omega rho(r)$ along with different forms of $kappa(mathcal{R},mathcal{T})-$function. This proved enough to derive a shape function of the form $b(r)=r_{0}left(frac{r_{0}}{r}right)^{1/omega}$. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through $kappa(mathcal{R},mathcal{T})$ function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.

According to the article on wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity, several conclusions can be drawn. Firstly, a solution with a constant redshift function leads to a wormhole that is asymptotically non-flat. Secondly, by assuming a linear equation of state $p(r)=omega rho(r)$ along with different forms of $kappa(mathcal{R},mathcal{T})-$function, the shape function of the wormhole can be derived as $b(r)=r_{0}left(frac{r_{0}}{r}right)^{1/omega}$. Thirdly, specific choices of the shape function consistent with the wormhole configuration requirements were explored. All the solutions fulfill the flare-out condition, are asymptotically flat, and supported by phantom energy. Furthermore, the length of the throat of the wormhole is affected by the coupling parameters through the $kappa(mathcal{R},mathcal{T})$ function. Finally, the average null energy condition is satisfied by all wormhole models, indicating that minimum exotic matter is required to open the wormhole throats.

## Future Roadmap

### Potential Challenges

- Validation of the proposed wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity through observation or experimental evidence
- Investigation of the stability and longevity of the wormhole solutions
- Exploration of the effects of other physical factors on the wormhole properties, such as rotation or electromagnetic fields

### Potential Opportunities

- Application of the derived wormhole solutions in $kappa(mathcal{R},mathcal{T})$ gravity to areas such as interstellar travel or teleportation
- Further development of the numerical method for generating the embedding surface and revolution of the wormhole
- Exploration of other $kappa(mathcal{R},mathcal{T})$ functions and their impacts on the shape and properties of wormholes

Overall, the study of wormholes in $kappa(mathcal{R},mathcal{T})$ gravity has provided valuable insights into their configurations and properties. While challenges remain in terms of validation and stability, there are also exciting opportunities for practical applications and further research in this field.

**Source:
arXiv:2403.19733v1**

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