Static and Dynamic Analysis of a Massless Scalar Field Coupled with a Class of Gravity Theories

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General static solutions for a massless scalar field coupled to a class of effectively 2-d gravity theories continuously connecting spherically symmetric d-dimensional Einstein gravity (d >3) and the CGHS model are analytically obtained. They include black holes and point scalar charge solutions with naked singularities, and are used to give an analytic proof of no-hair theorem. Exact scattering solutions in s-wave 4-d Einstein gravity are constructed as a generalization of corresponding static solutions. They show the existence of black hole formation threshold for square pulse type incoming stress-energy flux, above which trapped surfaces are dynamically formed. The relationship between this behavior and the numerically studied phase transition in this system choptuik is discussed.