Extended Black Hole Solutions in Self-interacting Brans-Dicke Theory

TL;DR

This paper develops new black hole solutions within self-interacting Brans-Dicke theory using an extended gravitational decoupling approach, exploring the effects of additional sources and scalar fields on the solutions.

Contribution

It introduces a novel method for constructing black hole solutions in Brans-Dicke theory with extended decoupling and analyzes the matter content of these solutions.

Findings

Three distinct solutions obtained for different decoupling parameters.

Two solutions satisfy energy conditions with normal matter.

Additional scalar field influences the properties of black hole solutions.

Abstract

In this paper, we formulate black hole solutions through extended gravitational decoupling scheme in the framework of self-interacting Brans-Dicke theory. The addition of a new source in the matter distribution increases the degrees of freedom in the system of field equations. Transformations in radial as well as temporal metric functions split the system into two arrays. Each array includes the effects of only one source (either seed or additional). The seed source is assumed to be a vacuum and the corresponding system is specified through the Schwarzschild metric. In order to construct a suitable solution of the second system, constraints are applied on the metric potentials and energy-momentum tensor of the additional source. We obtain three solutions corresponding to different values of the decoupling parameter in the presence of a massive scalar field. The extra source is classified as normal or exotic through energy conditions. It is found that two solutions agree with the energy bounds and thus have normal matter as their source.