Solution

ID: past-exam-of-the-general-relativity-ii-course-of-the-university-of-oxford/2015/2/b/ii/solution

If with , then
The curvature singularity remains at . At the static chart has a coordinate singularity, removed by the Eddington-Finkelstein coordinates above. The Kretschmann scalar there equals , which is finite. The coincident horizons form a degenerate Killing horizon, and its future outer branch is the event horizon of the extremal black hole. A double zero of does not remove the horizon.

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