The trans-Planckian problem and gravitational interactions

Abstract

The strong gravitational interaction of counter-propagating quantum field modes is of foundational importance to the trans-Planckian problem of black hole horizons. This article, in memory of Renaud Parentani, is primarily an exposition of Renaud's attempt, using perturbation theory, a large $N$ approximation, and spherical reduction, to capture a mechanism by which those interactions might quench the trans-Planckian near-horizon quantum field correlations. Before giving a detailed account of Renaud's calculation, the trans-Planckian problem is briefly introduced, and the paper concludes with a discussion of related issues and questions.

arXiv comment20 pages, 2 figures; contribution to Comptes Rendus. Physique - a special issue in memory of Renaud Parentani (the typesetting is more elegant in the Comptes Rendus version)

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