A new derivation of singularity theorems with weakened energy hypotheses

TY - JOUR

T1 - A new derivation of singularity theorems with weakened energy hypotheses

AU - Fewster, Chris

AU - Kontou, Eleni

N1 - © 2020 The Author(s). Published by IOP Publishing Ltd

PY - 2020/3/19

Y1 - 2020/3/19

N2 - 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.

AB - 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.

U2 - 10.1088/1361-6382/ab685b

DO - 10.1088/1361-6382/ab685b

M3 - Article

SN - 0264-9381

VL - 37

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 6

M1 - 065010

ER -