Nonlinear Scalarization of Schwarzschild Black Hole in Scalar-Torsion Teleparallel Gravity

We consider a scalar field coupled to the torsion in Teleparallel Gravity with a coupling function that does not allow for a tachyonic instability to occur, and it leads to the formation of new black holes with scalar hair. The scalarized black hole solutions are asymptotically flat, and they are studied under their thermodynamics, and we show that they are meta-stable solutions without phase transitions of first and second order. Also, we demonstrate the existence of distinct branches of solutions classified by the number of nodes of the scalar field. For the branches analysed, the scalarized solutions have lower free energy than the Schwarzschild black hole; therefore, they are always thermodinamically preferred. Also, we show that the scalarized black holes are entropically favoured compared to the Schwarzschild solution.