Rp = exp(1 + sqrt(1-a^2))
Rm = exp(1 - sqrt(1-a^2))
Hp = circle((0,0), Rp, color='black', thickness=2) + \
text(r'$\mathscr{H}$', (0.77*Rp, 0.77*Rp), color='black', fontsize=20)
Hm = circle((0,0), Rm, color='green', thickness=2) + \
text(r'$\mathscr{H}_{\rm in}$', (1.2*Rm, 1.05*Rm), color='green', fontsize=20)
R0 = circle((0,0), 1, color='darkorange', linestyle='dotted', thickness=3) + \
text(r'$r\!=\!0$', (1.1,-1.), color='darkorange', fontsize=16)
sing = circle((1,0), 0.1, color='red', fill=True) + \
circle((-1,0), 0.1, color='red', fill=True)
rminf = circle((0,0), 0.1, edgecolor='black', facecolor='white', fill=True)
region_label = text(r'${\rm I}$', (-1.2*Rp, 0.8*Rp), fontsize=20) + \
text(r'${\rm II}$', (-0.5*Rp, 0.4*Rp), fontsize=20) + \
text(r'${\rm III}$', (-0.3*Rm, 0.5*Rm), fontsize=20)
graph = ergo + Hp + Hm + R0 + sing + rminf + region_label