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T-duality is one of the features that sets string theory apart. Surprisingly, the
early observation by Rocek and Verlinde (1991) that horizons get mapped to
singularities has not received much attention. We will use Einstein-Maxwell
theory to show how T-duality rules are derived in a four-dimensional setting
and apply this result to obtain and analyse the T-duals of four-dimensional
spacetimes containing horizons as well as curvature singularities. While this
can be viewed as applying a solution-generating technique to Einstein-
Maxwell theory, an embedding of the solutions into string theory provides
additional insights into the nature of the singularities.