Black-bounce solution in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>-essence theories
C. F. S. Pereira, Denis C. Rodrigues, J. C. Fabris, Manuel E. Rodrigues
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, ${\mathrm{\ensuremath{\Sigma}}}^{2}={x}^{2}+{a}^{2}$. 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 the null energy condition $({\mathrm{NEC}}^{\ensuremath{\phi}})$. The Kretschmann scalar is regular in spacetime, and the geodesics are complete. The energy conditions are analyzed, verifying that the null $({\mathrm{NEC}}_{1}^{\ensuremath{\phi}})$ and dominant energy conditions $({\mathrm{DEC}}_{1}^{\ensuremath{\phi}})$ are violated inside and outside the event horizon. Finally, the extrinsic curvature method is applied to determine the sign of the mass on the junction surface.