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Physical Review D

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Black-bounce solution in $k$ -essence theories

Carlos F. S. Pereira ^*

Denis C. Rodrigues ^†

Júlio C. Fabris ^‡

Manuel E. Rodrigues ^§

Departamento de Física, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari, 514, Goiabeiras, 29060-900, Vitória, Espírito Santo, Brazil

Núcleo Cosmo-ufes and Departamento de Física, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari, 514, Goiabeiras, 29060-900, Vitória, Espírito Santo, Brazil

Núcleo Cosmo-ufes and Departamento de Física, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari, 514, Goiabeiras, 29060-900, Vitória, Espírito Santo, Brazil and National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Kashirskoe shosse 31, Moscow, Russia

Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará Campus Universitário de Abaetetuba, 68440-000, Abaetetuba, Pará, Brazil and Faculdade de Física, Programa de Pós-Graduação em Física, Universidade Federal do Pará, 66075-110, Belém, Pará, Brazil

^*carlos.f.pereira@edu.ufes.br
^†deniscr@gmail.com
^‡julio.fabris@cosmo-ufes.org
^§esialg@gmail.com

Phys. Rev. D 109, 044011 – Published 5 February, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.044011

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, $Σ^{2} = x^{2} + a^{2}$ . 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 $({NEC}^{ϕ})$ . The Kretschmann scalar is regular in spacetime, and the geodesics are complete. The energy conditions are analyzed, verifying that the null $({NEC}_{1}^{ϕ})$ and dominant energy conditions $({DEC}_{1}^{ϕ})$ 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.

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