On the classicality of bosonic stars

TL;DR

This paper argues that bosonic stars with sufficiently large mass can be accurately described as classical objects because their typical action greatly exceeds Planck's constant, making quantum effects negligible.

Contribution

It provides a generic argument demonstrating that bosonic stars with large maximum mass can be treated classically, extending the validity of classical descriptions to astrophysical scales.

Findings

Classical treatment is valid for bosonic stars with mass much greater than the Planck mass.

Typical action for such stars exceeds ^{76} times ^{76} imes ext{(mass ratio)}^2.

Classical approximation applies to astrophysical bosonic stars with masses  M_\u2192 M_.

Abstract

Because the Klein-Gordon and Proca equations involve $\hbar$, they describe quantum fields. Their solutions, however, may be treated as classical if their typical action obeys $S^{\rm typical}\gg \hbar$. 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 ${\mathcal{S}^{\rm typical}}/{\hbar}\gtrsim \left({M^{\rm max}}/{M_{\rm Pl}}\right)^2\sim 10^{76}\left({M^{\rm max}}/{M_\odot}\right)^2$, where $M^{\rm max}$ is the maximal bosonic star mass of the particular model and $M_{\rm Pl}$ is the Planck mass. Thus, for models allowing $M^{\rm max}\gg M_{\rm Pl}$ and for solutions with mass $\sim M^{\rm max}$, the classical treatment is legitimate, which includes masses in the astrophysical interesting range $\gtrsim M_\odot$.