 Solution

On $\theta =\lambda =0$, the radial function $r\Delta =r^3+a^{2}r-\mu$ is strictly increasing and has the single positive root $r_{+}$. The curvature invariant diverges at $r=0$, and $g^{rr}=\Delta /\Sigma <0$ immediately inside the horizon, so this is a spacelike singularity. The maximally extended Penrose diagram therefore has the Schwarzschild form: two asymptotically flat exterior diamonds separated by future and past event horizons, with a spacelike future singularity above the black-hole regions and a spacelike past singularity below the white-hole regions. A collapse spacetime retains one exterior, the future horizon, and the future spacelike singularity.