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We study a general flat space/boson star transition model in quasi-localensemble through approaches familiar from holographic superconductor theories.We manage to find a parameter $\psi_{2}$, which is proved to be useful indisclosing properties of phase transitions. In this work, we explore effects ofthe scalar mass, scalar charge and St$\ddot{u}$ckelberg mechanism on thecritical phase transition points and the order of transitions mainly frombehaviors of the parameter $\psi_{2}$. We mention that properties oftransitions in quasi-local gravity are strikingly similar to those inholographic superconductor models. We also obtain an analytical relation$\psi_{2}\varpropto(\mu-\mu_{c})^{1/2}$, which also holds for the condensedscalar operator in the holographic insulator/superconductor system inaccordance with mean field theories.

Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors