Kasner eons with matter: holographic excursions to the black hole singularity

Recent work has shown that introducing higher-curvature terms to
the Einstein-Hilbert action causes the approach to a space-like
singularity to unfold as a sequence of Kasner eons. Each eon is dominated
by emergent physics at an energy scale controlled by higher-curvature
terms of a given order, transitioning to higher-order eons as the
singularity is approached. In this talk, I will first demonstrate how the
presence of matter dramatically modifies the physics of these eons
compared to the vacuum case. I will illustrate this by considering a
family of quasi-topological gravities of arbitrary order minimally coupled
to a scalar field. Then, I will explain the imprints of these eons on
holographic observables. Specifically, I will demonstrate that the
behavior of the thermal a-function, two-point functions of heavy
operators, and holographic complexity can capture distinct signatures of
the eons, making them valuable tools for diagnosing stringy effects near
black hole singularities.