Nonlinear instability and scalar clouds of spherical exotic compact objects in scalar-Gauss-Bonnet theory

In this work, we present a new type of scalar clouds supported by spherically symmetric horizonless compact objects in the scalar-Gauss-Bonnet theory. Unlike the previous spontaneous scalarization that is triggered by the tachyonic instability, our scalarization arises from a nonlinear instability that is non-spontaneous. We explore two types of boundary conditions for the scalar field at the surface of the compact objects and find an infinite countable set of scalar clouds characterized by the number of nodes for both cases. Our study demonstrates that boundary conditions have a significant impact on the formation of scalar clouds. Specifically, for the Dirichlet boundary condition, scalarization is more likely to occur for compact objects with medium radii and becomes harder for ultra-compact and large ones. Conversely, for the Robin boundary condition, scalarization is easier for more compact objects.