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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. The purpose of this paper is twofold. First, we demonstrate that the inclusion of matter dramatically modifies the physics of eons compared to the vacuum case. We illustrate this by considering a family of quasi-topological gravities of arbitrary order minimally coupled to a scalar field. Second, we investigate Kasner eons in the interior of black holes with field theory duals and analyze their imprints on holographic observables. We show that the behavior of the thermala-function, two-point functions of heavy operators, and holographic complexity can capture distinct signatures of the eons, making them promising tools for diagnosing stringy effects near black hole singularities. 

A<sc>bstract</sc> We study holographic renormalization group (RG) flows perturbed by a shock wave in dimensionsd≥ 2. The flows are obtained by deforming a holographic conformal field theory with a relevant operator, altering the interior geometry from AdS-Schwarzschild to a more general Kasner universe near the spacelike singularity. We introduce null matter in the form of a shock wave into this geometry and scrutinize its impact on the near-horizon and interior dynamics of the black hole. Using out-of-time-order correlators, we find that the scrambling time increases as we increase the strength of the deformation, whereas the butterfly velocity displays a non-monotonic behavior. We examine other observables that are more sensitive to the black hole interior, such as the thermala-function and the entanglement velocity. Notably, thea-function experiences a discontinuous jump across the shock wave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. This jump is interpreted as a ‘cosmological time skip’ which arises from an infinitely boosted length contraction. The entanglement velocity exhibits similar dependence to the butterfly velocity as we vary the strength of the deformation. Lastly, we extend our analyses to a model where the interior geometry undergoes an infinite sequence of bouncing Kasner epochs. 

A bstract We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT 2 degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence emerging when the boundary interval is too big relative to the black hole’s inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT 2 and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.