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arXiv · 1611.07981

Non-Gaussian ground-state deformations near a black-hole singularity

Stefan Hofmann·Marc Schneider
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Abstract

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black-holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows to probe the space-like singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black-holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The clash of completeness cultures as exemplified with black holes is discussed.

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Stefan Hofmann, Marc Schneider. 2016-11-23. Non-Gaussian ground-state deformations near a black-hole singularity. https://doi.org/10.1103/physrevd.95.065033

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