Black-bounce solutions in a k-essence theory under the effects of bumblebee gravity

Abstract

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 ${\Sigma }^2=x^2+a^2$ and complement the proposal with a new black-bounce model for the area functions ${\Sigma }_1^2=\sqrt{x^4+d^4}$. 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.

15 pages, 7 figures. Comments are welcome. V2: Minor modifications to match published version

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• Gravitational aspects of a new bumblebee black hole
• Sources of matter for wormholes in a k-essence theory
• Primordial black hole formation in k-inflation models