Scalarized black holes in new massive gravity dressed by a nonminimally coupled scalar

We investigate scalarized black holes in newmassive gravity dressed by a nonminimally coupled scalar. For this purpose, we find the Gregory-Laflamme (GL) and tachyonic instability bounds of bald BTZ black hole expressed in terms of m(2) a massive spin-2 parameter and a a scalar coupling parameter to Ricci scalar by making use of the linearized theory around black hole. On the other hand, we obtain a solution bound of 0.161 < alpha < 3/16 for achieving non-BTZ black holes with scalar hair analytically and a thermodynamic bound of 1/8 < alpha < 13/80 for obtaining consistent thermodynamic quantities. Without imposing the GL instability bound (m(2) < 1/(2)l(2)), we find a very narrow bound of 0.161 < alpha < 0.1625 which is located inside tachyonic instability bound of alpha > 1/8 + m(Phi)(2) l(2)/6 for obtaining scalarized black holes where m(Phi)(2) is a scalar mass parameter.