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A new derivation of singularity theorems with weakened energy hypotheses

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JournalClassical and Quantum Gravity
DateAccepted/In press - 20 Dec 2019
DateE-pub ahead of print - 18 Feb 2020
DatePublished (current) - 19 Mar 2020
Issue number6
Early online date18/02/20
Original languageEnglish


The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri's equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by Quantum Energy Inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply.

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© 2020 The Author(s). Published by IOP Publishing Ltd

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