Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new derivation of singularity theorems with weakened energy hypotheses   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.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol