Black-bounce solution in $k$-essence theories

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.
Comment: 13 pages, 15 figures