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

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 $\beta \to 0$ 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.

10 pages, 6 figures, final version accepted for publication in Modern Physics Letters A

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• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• Electromagnetic Generalized Quasi-topological gravities in $(2+1)$ dimensions
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• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• Three-dimensional black holes via Noether symmetries
• Quasinormal modes of charged BTZ black holes
• On regular charged black holes in three dimensions
• Born-Infeld Thin-shell Wormholes Supported by Generalized Cosmic Chaplygin Gas