## A collapse singularity theorem permitting achronologies

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- Written by Martin Lesourd

A new collapse-type singularity theorem is formulated. The premise of the theorem involves various semi-global geometric conditions whose purpose it is to represent a region of strong gravity that is surrounded by an event horizon. These conditions, though relatively specific, may be argued to be natural from what is known of black holes and the various trapped surfaces associated with them. The restriction on causal structure is that the relevant region be marginally less pathological than non-totally vicious. This is weaker than the chronology assumption of the Hawking-Penrose theorem though comparable to that used in recent strengthened versions thereof. The method of proof is different in that it makes use of recent work on causal structure by Minguzzi, which, in particular, permits bypassing the generic timelike and or null conditions. Another significant feature is that the theorem's conclusion permits locating future incomplete null geodesics within the strong gravity region. An important role is also played by Minguzzi's proposal for the boundary of a chronology violating set.