M^*$, the spacetime has a space-like singularity analogous to the Schwarzschild black hole, whilst it has a time-like singularity. Note that the time-like singularity arising from $M< M^*$ is different from that in the Reissner-Nordstr\"om black hole which has a $1/r^8$ divergence. When $M=M^*$, the solution has a conical singularity where $g_{tt}$ is non-vanishing. Thus, for spherically-symmetric solutions with $k=1$, we have the following classifications: \begin{itemize} \item $Q>\ft{2}{b}$: \begin{itemize} \item $M>M^*$: Schwarzschild-like black hole with space-like $1/r^6$ singularity. \item $M=M^*$: black hole with space-like $1/r^4$ conical singularity. \item $M_{\rm ext}M^*$: Schwarzschild-like black hole with space-like $1/r^6$ singularity. \item $M=M^*$: naked time-like $1/r^4$ singularity. \item $MM^*$: Schwarzschild-like black hole with space-like $1/r^6$ singularity. \item $M\!=\!M^*$: a null singularity where the horizon and curvature singularity \mbox{coincide}. \item $M2/b$. \pagebreak As mentioned earlier, the matter field $A$ is singularity free at $r=0$, one would then expect that there exists a parameter like $M=M^*$ such that the spacetime solution is free from singularity. However, there is a singularity for the general solutions. To understand this phenomenon, we note from~(\ref{eq9}) that the matter energy-momentum tensor is \be T^{\mu\nu}_{\rm mat}=-\frac{b^2}{2} \frac{\sqrt{-h}}{\sqrt{-g}} \,\left(h^{-1} \right)^{(\mu\nu)}\,. \ee It follows that even if $h_{\mu\nu}$ is non-singular and non-vanishing at $r=0$, the matter energy-momentum tensor diverges at $r=0$ since $\sqrt{-g}$ vanishes there. The singularity however becomes much milder, and the solution with $Q<2/b$ and $M=M^*$ may be viewed as a quasi-soliton. ]]>