https://doi.org/10.1140/epjc/s10052-025-14582-3
Regular Article - Theoretical Physics
Generalized scalar field models in the presence of impurities
1
Departamento de Física, Universidade Federal da Paraíba, 58051-970, João Pessoa, PB, Brazil
2
Departamento de Biotecnologia, Universidade Federal da Paraíba, 58051-900, João Pessoa, PB, Brazil
3
Departamento de Ciências Exatas, Universidade Federal da Paraíba, 58297-000, Rio Tinto, PB, Brazil
Received:
18
March
2025
Accepted:
25
July
2025
Published online:
4
August
2025
We study generalized scalar field models coupled to impurities in Minkowski spacetime with arbitrary dimensions. The investigation concerns a class of models that depends explicitly on the spacetime coordinates and also, it reveals the presence of a second-order tensor that can have null divergence if a first-order equation and a constraint are satisfied. We obtain the conditions to get compatibility between the equation of motion and the first-order equation, within a framework that is also used in the static case, to show that the introduction of an auxiliary function may allow to describe the energy density of the solution as a divergence. Stability of the solution under rescale of argument, translation in the space and small fluctuations are also fully investigated. We further illustrate the procedure considering the canonical model and also, the k-field and Born–Infeld-like models. The results show that stable solutions can be obtained in arbitrary dimensions, and the stability seems to be related to the first-order equation that emerges from imposing null divergence of the aforementioned tensor.
© The Author(s) 2025
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