Kasner Epochs, Eras and Eons

Abstract

As shown in the classic work of Belinski, Khalatnikov and Lifshitz, the approach to a generic space-like singularity in general relativity consists of a sequence of eras and epochs in which the metric is locally Kasner, connected by brief transitions. When quantum gravity effects are included, we argue that a new type of transition arises, giving rise to Kasner eons: periods which are dominated by emergent physics at each energy scale. We comment on the different ways in which the Einsteinian eon may come to an end and show explicitly how additional Kasner eons arise in the interior of a black hole solution due to higher-derivative corrections.

13 pages, 2 figures; v2: minor changes, title modified to comply with journal criteria; version to appear in PRD