Instantaneous Cauchy surfaces, topology change, and exploding black holes

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Abstract
Instantaneous Cauchy surfaces are defined and several of their properties are given. Instantaneous Cauchy surfaces are achronal surfaces whose Cauchy development interiors are maximal on the set of all achronal surfaces. It is shown that topology changes in such surfaces always result in nonempty future Cauchy horizons and departures from global hyperbolicity. It is also shown that the structure which is usually assumed for the background spacetime of a self‐consistent exploding black hole implies a topology change in instantaneous Cauchy surfaces.
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