MG12 - Talk detail
 

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Refining trapped surfaces

Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increasingly (future, respectively past) trapped surfaces generate surfaces which are more trapped in a (future, respectively past) causal variation, with three types: in any such causal variation, along the expansion vector, and in some such causal variation. This suggests a definition of doubly outer trapped surface involving two independent curvatures. This in turn suggests a definition of involute trapped surface. Adding a weaker condition, the eight conditions form an interwoven hierarchy, with four independent relations which assume the null energy condition, and another holding in a special case of symmetric curvature.

Wormhole dynamics

A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or "flaring-out". The null energy condition must be violated at a wormhole mouth. Zeroth, first and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.

Formation and evaporation of regular black holes

Regular space-times are given which describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region. The static region is Bardeen-like, supported by finite density and pressures, vanishing rapidly at large radius and behaving as a cosmological constant at small radius. The dynamic regions are Vaidya-like, with ingoing radiation of positive energy flux during collapse and negative energy flux during evaporation, the latter balanced by outgoing radiation of positive energy flux and a surface pressure at a pair creation surface. The black hole consists of a compact space-time region of trapped surfaces, with inner and outer boundaries which join circularly as a single smooth trapping horizon.

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