In the present study, we analyze the effects of violation of Lorentz symmetry for black-bounce solutions in a $k$-essence theory that has the form of a power law for the configuration $n=1/3$. We perform such analysis for a known model explored in previous work, ${\mathrm{\Sigma }}^2=x^2+a^2$, and complement the proposal with a new black-bounce model for the area functions, ${\mathrm{\Sigma }}_1^2=\sqrt{x^4+d^4}$. This model has the Schwarzschild–de Sitter asymptomatic behavior for $x\to -\infty$, and we investigate the scalar field, potential, and energy conditions for both models. We have shown that the violation of Lorentz symmetry can be generated through $k$-essence without the need for an additional field. These results corroborate the validation of other previously investigated wormhole solutions.

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• Classical black holes
• General relativity equations & solutions
• Singularities In general relativity