New sources of ghost fields in $k$-essence theories for black-bounce solutions

TL;DR

This paper explores new ghost scalar field configurations within $k$-essence theories for black-bounce solutions, confirming their consistency and validating previous wormhole models without altering energy conditions.

Contribution

It generalizes ghost field configurations in $k$-essence theories for Simpson-Visser metrics, providing new solutions and verifying their physical viability.

Findings

All equations of motion are satisfied for new ghost field configurations.

Energy conditions remain unchanged despite new ghost field proposals.

Validates previous wormhole solutions within this framework.

Abstract

In the present study, we generalize the possible ghost field configurations within the framework of $k$-essence theory to the Simpson-Visser metric area function $\Sigma^2=x^2+a^2$. Our analysis encompasses field configurations for the region-defined metric function $dA_\pm$ as well as the general solution that asymptotically behaves as Schwarzschild-de Sitter for $x\to-\infty$. Specifically, we investigate two scalar field configurations and define the associated potential for each one. Through rigorous calculations, we verify that all equations of motion are satisfied. Notably, our findings indicate that even when proposing new configurations of ghost scalar fields, the energy conditions remain unchanged. This result serves to validate the wormhole solutions obtained in previous studies.