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Motivated by the recent progress in solving the large charge sector ofconformal field theories, we revisit the mass-charge relation of boson starsasymptotic to global AdS. We construct and classify a large number ofelectrically charged boson star solutions in a toy model and two supergravitymodels arising from the $SU(3)$ and $U(1)^4$ truncation of $D=4$ $SO(8)$ gaugedmaximal supergravity. We find a simple ansatz for the chemical potential thatcan fit the numerical data in striking accuracy for the full range of charge.Combining with the first law of thermodynamics, we can then evaluate the massas a function of the charge and obtain the free energy in the fixed chargeensemble. We show that in the toy model, the ground state can be either theextremal RN black hole or the boson stars depending on the parameter region.For the $SU(3)$ truncation, there always exists a boson star that has smallerfree energy than the extremal RN black hole, in contrast to the $U(1)^4$ modelwhere the extremal RN black hole is always the ground state. In all models, forboson star solutions with arbitrarily large charge, we show that the largecharge expansion of the mass reproduces the same structure exhibited in the CFTside.

Revisiting the AdS Boson Stars: the Mass-Charge Relations