Underlying mechanisms of the scalarization phase transition

Spontaneous scalarization is the formation of stable scalar field clouds around compact objects in scalar-tensor theories. This phenomenon has seen intense interest due to the potentially observable large gravitational wave signatures it leads to. We have long known scalarization to be a form of phase transition, but it is only recently that extensive computational studies have shown it to be more likely a first-order phase transition rather than a second-order one. This has important implications for testing the idea through novel observational channels. Here, we study the scalarization phase transition from first principles rather than through the phenomenological models of recent work. Our approach provides a fundamental understanding of the nonlinear solutions of the theory and elucidates the mechanism behind the dominance of first-order scalarization in the parameter space. We develop the analytical tools to investigate different forms of scalarization arising from various coupling terms in scalar-tensor theories, saving significant computational resources in upcoming studies.