On the classicality of bosonic stars

Abstract

Because the Klein–Gordon and Proca equations involve ℏ, they describe quantum fields. Their solutions, however, may be treated as classical if their typical action obeys 𝑆typical≫ℏ. This is possible due to their bosonic nature, allowing states with many particles. We show, by generic arguments, that the typical action for such bosonic stars is 𝒮typical/ℏ≳(𝑀max/𝑀Pl)2∼1076(𝑀max/𝑀⊙)2, where 𝑀max is the maximal bosonic star mass of the particular model and 𝑀Pl is the Planck mass. Thus, for models allowing 𝑀max≫𝑀Pl and for solutions with mass ∼𝑀max, the classical treatment is legitimate, which includes masses in the astrophysical interesting range ≳𝑀⊙.