We make an analysis of $Q$-balls and boson stars using catastrophe theory, as an extension of the previous work on $Q$-balls in flat spacetime. We adopt the potential $V_3(\varphi )=\frac{m^2}{2}{\varphi }^2-\mu {\varphi }^3+\lambda {\varphi }^4$ for $Q$-balls and that with $\mu =0$ for boson stars. For solutions with $|g^{rr}-1|\sim 1$ at its peak, stability of $Q$-balls has been lost regardless of the potential parameters. As a result, phase relations, such as a $Q$-ball charge versus a total Hamiltonian energy, approach those of boson stars, which gives us a unified picture of $Q$-balls and boson stars.

• Received 23 February 2010

DOI:https://doi.org/10.1103/PhysRevD.81.124041