Singularity theorems from weakened energy conditions

Abstract

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

arXiv commentv3 18 pages. Minor correction to the proof of Lemma 3.1; results are unchanged. Final version to appear in Class Quantum Grav

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