Abstract
We present black hole solutions in (2+1)-dimensional Einstein’s theory of gravity coupled with Born–Infeld (BI) nonlinear electrodynamic and a massless self-interacting scalar field. The model has five free parameters: mass [Formula: see text], cosmological constant [Formula: see text], electric [Formula: see text] and scalar [Formula: see text] charges and BI parameter [Formula: see text]. To attain exact solution for such a highly nonlinear system we adjust, i.e. finely tune, the parameters of the theory with the integration constants. In the limit [Formula: see text], 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 (NED) field in 2+1 dimensions without searching for exact solutions.
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