On the classicality of bosonic stars

Abstract

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

arXiv comment11 pages; Essay written for the Gravity Research Foundation 2022 Awards for Essays on Gravitation and selected for Honorable Mention

References in corpus (7)

• TOPICAL REVIEW: General relativistic boson stars
• Dynamical Boson Stars
• Proca Stars: gravitating Bose-Einstein condensates of massive spin 1 particles
• GW190521 as a merger of Proca stars: a potential new vector boson of $8.7\times 10^{-13}$ eV
• The imitation game: Proca stars that can mimic the Schwarzschild shadow
• Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions
• Asymptotically flat spinning scalar, Dirac and Proca stars

Cited by in corpus (4)

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• Piercing of a solitonic boson star by a black hole