= Solution
There is only one zero of $f$, at $r=2m$, and the <Kruskal–Szekeres coordinates> give four quadrants. Both exterior quadrants have $r>2m$, while the future and past interior quadrants have $0<r<2m$. The <tortoise coordinate> is finite at $r=0$: for $q>0$, $dr_*/dr\sim-\sqrt q\,r^{1/2}/(2m)$, and for $q=0$ it is $-r/(2m)$. Throughout each interior $g^{rr}=f<0$, so constant-$r$ hypersurfaces are spacelike. The assumed <curvature singularity> at $r=0$ therefore forms a spacelike future boundary in the black-hole region and a spacelike past boundary in the white-hole region. At infinity, $f\to1$ and $R/r\to1$, giving two standard asymptotically flat ends.
The resulting <Penrose diagram> is the same four-region causal diagram as the maximal <Schwarzschild spacetime>:
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/iii/paper-56-penrose.png]
{title=Maximal extension of the charged single-horizon geometry, with two exteriors, a black hole, a white hole and spacelike singularities}
Each exterior has its own <past null infinity>, <future null infinity>, spatial infinity and timelike infinities. The future and past <event horizons> intersect on the <bifurcation surface>. The diagram describes the eternal analytic solution; a spacetime formed by collapse need not contain its white-hole region or second exterior.
Unlike a nonextreme <Reissner-Nordstrom black hole>, this electrically charged solution has \b[one horizon and spacelike singularities, with no inner Cauchy horizon]. A nonextreme Reissner-Nordstrom solution has two distinct horizons, including an inner <Cauchy horizon>, and a timelike singularity; its ideal maximal extension contains an infinite sequence of exterior and interior blocks. Charge by itself does not determine this causal structure: the metric and field equations of the gravitational theory matter.
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