Nonlinearly charged dilatonic black holes and their Brans-Dicke counterpart: Energy dependent spacetime

TL;DR

This paper explores the coupling of dilaton fields with electrodynamics in energy-dependent spacetimes, deriving analytical solutions for dilaton-Born-Infeld and Brans-Dicke-Born-Infeld theories while ensuring compatibility with Brans-Dicke theory.

Contribution

It introduces a suitable Lagrangian for dilaton-electrodynamics coupling that satisfies compatibility with Brans-Dicke theory and applies it to obtain analytical solutions in energy-dependent spacetime.

Findings

Derived analytical solutions for dilaton-Born-Infeld and Brans-Dicke-Born-Infeld theories.

Established criteria for coupling scalar fields with electrodynamics in dilaton gravity.

Ensured the Lagrangian's compatibility with Brans-Dicke theory and special cases.

Abstract

Regarding the wide applications of dilaton gravity in the presence of electrodynamics, we introduce a suitable Lagrangian for the coupling of dilaton with gauge field. There are various Lagrangians which show the coupling between scalar fields and electrodynamics with correct special situations. In this paper, taking into account conformal transformation of Brans-Dicke theory with an electrodynamics Lagrangian, we show that how scalar field should couple with electrodynamics in dilaton gravity. In other words, in order to introduce a correct Lagrangian of dilaton gravity, one should check at least two requirements: compatibility with Brans-Dicke theory and appropriate special situations. Finally, we apply the mentioned method to obtain analytical solutions of dilaton-Born-Infeld and Brans-Dicke-Born-Infeld theories with energy dependent spacetime.