The critical baryon number and critical ADM energy depend on $\varphi_0$. For a baryon number smaller than the critical one, one stable equilibrium solution exists, while, for a baryon number larger than the critical one, no stable equilibrium solution exists. In particular, for $\varphi_0=0$, the stable equilibrium solution is completely identical to that in general relativity. The behavior of the scalar charge and scalar susceptibility near the critical baryon number is explained by the form of the potential function of the fold catastrophe.

For $\beta\alt-4.35$, the cusp catastrophe does occur while the fold catastrophe also occurs. For $\beta\alt-4.9$, there is some critical value of the scalar field, $\varphi_0^{crit}>0$. If $|\varphi_0|>\varphi_0^{crit}$, there is only one critical number $N^{crit1}$ that depends on $\varphi_0$. For $N<N^{crit1}$, one stable equilibrium solution exists, while, for $N>N^{crit1}$, no stable equilibrium solution exists. If $0<|\varphi_0|<\varphi_0^{crit}$, there are three critical baryon numbers $N^{crit1}>N^{crit2}>N^{crit3}$. For $N<N^{crit3}$ or $N^{crit2}<N<N^{crit1}$, only one stable equilibrium solution exists. For $N^{crit3}<N<N^{crit2}$, two distinct stable equilibrium solutions exist and they do not agree with those in general relativity even for the limit $\varphi_0\to 0$. The almost general relativistic branch is unstable for $N>N^{crit2}$. For $N>N^{crit1}$, however, no stable equilibrium solution exists. If $\varphi_0=0$, the sequence 