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Abstract
Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, there are models that do not satisfy the SEC and therefore lie outside the scope of Hawking's hypotheses, an important example being the massive KleinGordon field. Here we derive lower bounds on local averages of the EED for solutions to the KleinGordon equation, allowing nonzero mass and nonminimal coupling to the scalar curvature. The averages are taken along timelike geodesics or over spacetime volumes, and our bounds are valid for a range of coupling constants including both minimal and conformal coupling. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawkingtype singularity theorem for solutions to the EinsteinKleinGordon theory, asserting that solutions with sufficient initial contraction at a compact Cauchy surface will be future timelike geodesically incomplete.
Original language  English 

Article number  121 
Number of pages  24 
Journal  General Relativity and Gravitation 
Volume  50 
DOIs  
Publication status  Published  8 Sep 2018 
Bibliographical note
© The Author(s) 2018Projects
 1 Finished

QuEST: Quantum Energy Conditions and Singularity Theorems
1/09/17 → 31/08/19
Project: Research project (funded) › Research