Abstract
In this work we study the 2+1-Einstein–Klein–Gordon system in the framework of Gravitational Decoupling. We associate the generic matter decoupling sector with a real scalar field so we can obtain a constraint which allows us to close the system of differential equations. The constraint corresponds to a differential equation involving the decoupling functions and the metric of the seed sector and will be independent of the scalar field itself. We show that when the equation admits analytical solutions, the scalar field and the self-interacting potential can be obtained straightforwardly. We found that, in the cases under consideration, it is possible to express the potential as an explicit function of the scalar field only for certain particular cases corresponding to limiting values of the parameters involved.
Highlights
As a theory of gravitation for spacetime, Einstein’s theory of General Relativity is considered one of the most successful theories in sciences, with a wide variety of predictions, many of them in cosmology, interpreting the dynamics of the universe
We identify the generic source which arises in the framework of Gravitational Decoupling (GD) [25] by the Minimal Geometric Deformation (MGD) approach with the matter sector associated with the scalar field
In the previous section we reduced the problem of solving the Einstein–Klein–Gordon system to seek for solutions of the constraint involving the decoupling function f through the MGD approach
Summary
As a theory of gravitation for spacetime, Einstein’s theory of General Relativity is considered one of the most successful theories in sciences, with a wide variety of predictions, many of them in cosmology, interpreting the dynamics of the universe. We identify the generic source which arises in the framework of Gravitational Decoupling (GD) [25] by the Minimal Geometric Deformation (MGD) approach with the matter sector associated with the scalar field (for implementation in 3 + 1 and 2 + 1 dimensional spacetimes see [26,27,28,29,30,31,32,33,34,35,36,37,38,39] and references therein).
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