Black-bounce solution in $k$-essence theories

TL;DR

This paper constructs regular black-bounce solutions within $k$-essence theories, analyzing their geometric properties, energy conditions, and scalar field behavior, revealing phantom characteristics and complete geodesics.

Contribution

It introduces new black-bounce configurations in $k$-essence theories with regular metrics and scalar fields, extending the understanding of such solutions with detailed energy condition analysis.

Findings

Kretschmann scalar is regular everywhere.

Null and dominant energy conditions are violated inside and outside the horizon.

Solutions exhibit phantom behavior due to NEC violation.

Abstract

In the present work, we construct black-bounce configurations in the context of $k$-essence theory. The solutions have a regular metric function at the origin. The area metric function is linked to the black-bounce area initially considered by Simpson-Visser, $\Sigma^2=x^2+a^2$. Subsequently, the expressions for the scalar field and scalar potential corresponding to the found solutions are determined, exhibiting phantom behavior everywhere due to violation of Null Energy Condition $(NEC^\phi)$. The Kretschmann scalar is regular throughout spacetime, and the geodesics are complete. The energy conditions are analyzed, verifying that the null $(NEC^\phi_1)$ and dominant energy conditions $(DEC^\phi_1)$ are violated inside and outside the event horizon. Finally, the extrinsic curvature method was applied to determine the sign of the mass on the junction surface.