$2+1$ Einstein-Klein-Gordon black holes by gravitational decoupling

TL;DR

This paper explores 2+1 dimensional Einstein-Klein-Gordon black holes using gravitational decoupling, deriving solutions for scalar fields and potentials under specific conditions, advancing understanding of lower-dimensional gravity models.

Contribution

It introduces a method to obtain analytical solutions for scalar fields and potentials in 2+1 Einstein-Klein-Gordon systems via gravitational decoupling.

Findings

Analytical solutions for scalar fields obtained in specific cases.

Explicit potential functions derived for certain parameter limits.

Demonstrates the feasibility of decoupling approach in lower-dimensional gravity.

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 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.