Nonlinear scalarization of Schwarzschild black holes 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 metastable 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 analyzed, the scalarized solutions have lower free energy than the Schwarzschild black hole; therefore, they are always thermodynamically preferred. Also, we show that the scalarized black holes are entropically favored compared to the Schwarzschild solution.