Nonlinear black hole scalarization in multi-scalar Gauss-Bonnet gravity

A process called nonlinear scalarization was recently demonstrated to exist for black holes in scalar-Gauss-Bonnet gravity. Contrary to the standard spontaneous scalarization, the nonlinear scalarization is a process which allows for a Schwarzschild black hole and a scalarized black hole, both linearly stable, to coexist. We extend the search for black holes with nonlinear scalarization in the case of multi-scalar Gauss-Bonnet gravity - a class of theories which allow for hairy compact objects with vanishing scalar charge, hence, there are no constraints from the binary pulsar observations. We demonstrate numerically the existence of such black hole solutions with nonlinear scalarization in the multi-scalar Gauss-Bonnet theories with exponential coupling function which is of fourth leading order in the scalar field.