Einstein-Born-Infeld black holes with a scalar hair in three-dimensions

TL;DR

This paper constructs exact black hole solutions in three-dimensional Einstein gravity coupled with Born-Infeld electrodynamics and a scalar field, exploring their properties and limits, and establishing a general scalar-tensor framework.

Contribution

It provides new exact solutions for 2+1-dimensional black holes with nonlinear electrodynamics and scalar hair, including a detailed analysis of their thermodynamics and a general scalar-tensor formulation.

Findings

Exact black hole solutions with scalar hair and nonlinear electrodynamics.

Hawking temperature dependence on tuned parameters.

Recovery of Einstein-Maxwell-Scalar results in the limit .

Abstract

We present black hole solutions in $2+1-$dimensional Einstein's theory of gravity coupled with Born-Infeld nonlinear electrodynamic and a massless self-interacting scalar field. The model has five free parameters: mass $M$, cosmological constant $\ell $, electric $q$ and scalar $r_{0}$ charges and Born-Infeld parameter $\beta $. To attain exact solution for such a highly non-linear system we adjust, i.e. finely tune, the parameters of the theory with the integration constants. In the limit $\beta \rightarrow 0$ we recover the results of Einstein-Maxwell-Scalar theory, obtained before. The self interacting potential admits finite minima apt for the vacuum contribution. Hawking temperature of the model is investigated versus properly tuned parameters. By employing this tuned-solution as basis, we obtain also a dynamic solution which in the proper limit admits the known solution in Einstein gravity coupled with self-interacting scalar field. Finally we establish the equations of a general scalar-tensor field coupled to nonlinear electrodynamics field\ in $2+1-$dimensions without searching for exact solutions.