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Two modern programs involving analogies between general relativity and electro-magnetism, gravito-electromagnetism (GEM) and the classical double copy (CDC), induce electromagnetic potentials from specific classes of spacetime metrics. We demonstrate such electromagnetic potentials are typically gauge equivalent to Killing vectors present in the spacetime, long known themselves to be analogous to electromagnetic potentials. We utilize this perspective to relate the Type D Weyl double copy to the Kerr-Schild double copy without appealing to specific coordinates. We analyze the typical assumptions taken within Kerr-Schild double copies, emphasizing the role Killing vectors play in the construction. The basis of the GEM program utilizes comparisons of tidal tensors between GR and EM; we perform a more detailed analysis of conditions necessary for equivalent tidal tensors between the theories, and note they require the same source prescription as the classical double copy. We discuss how these Killing vector potentials relate to the Weyl double copy, in particular there must a relation between the field strength formed from the Killing vector and the Weyl tensor. We consider spacetimes admitting a Killing-Yano tensor which provide a particularly insightful example of this correspondence. This includes a broad class of spacetimes, and provides an explanation for observations regarding the splitting of the Weyl tensor noted when including sources. 

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<sc>bstract</sc> Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In this work, we aim to understand generalized complexities in the framework of Lorentzian threads. We reformulate the problem in terms of thread distributions and measures and present a program to calculate the infinite family of codimension-one observables. We also outline a path to understand, using threads, the more subtle case of codimension-zero observables. 

A<sc>bstract</sc> We use the radial null energy condition to construct a monotonica-function for a certain type of non-relativistic holographic RG flows. We test oura-function in three different geometries that feature a Boomerang RG flow, characterized by a domain wall between two AdS spaces with the same AdS radius, but with different (and sometimes direction-dependent) speeds of light. We find that thea-function monotonically decreases and goes to a constant in the asymptotic regimes of the geometry. Using the holographic dictionary in this asymptotic AdS spaces, we find that thea-function not only reads the fixed point central charge but also the speed of light, suggesting what the correct RG charge might be for non-relativistic RG flows. 

A<sc>bstract</sc> We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order ofN, the standard result for theq-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter,k. We present an algorithm to sum the diagrams at any given order of 1/(kq)ⁿ. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finiteNbecomes more significant for larger values ofN. 

A<sc>bstract</sc> We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value ofNout of reach of current numerical simulations. 

A bstract We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of N Majorana fermions coupled by random q -body interactions. The degree of sparseness is captured by a regular hypergraph in such a way that the Hamiltonian contains exactly k N independent terms. We improve on the theoretical understanding of the sparseness property by using known measures of hypergraph expansion. We show that the sparse version of the two coupled SYK model is gapped with a ground state close to a thermofield double state. Using Krylov subspace and parallelization techniques, we simulate the system for q = 4 and q = 8. The sparsity of the model allows us to explore larger values of N than the ones existing in the literature for the all-to-all SYK. We analyze in detail the two-point functions and the transmission amplitude of signals between the two systems. We identify a range of parameters where revivals obey the scaling predicted by holography and signals can be interpreted as traversing the wormhole. 

A bstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling. 

A bstract In the context of holography, entanglement entropy can be studied either by i) extremal surfaces or ii) bit threads, i.e., divergenceless vector fields with a norm bound set by the Planck length. In this paper we develop a new method for metric reconstruction based on the latter approach and show the advantages over existing ones. We start by studying general linear perturbations around the vacuum state. Generic thread configurations turn out to encode the information about the metric in a highly nonlocal way, however, we show that for boundary regions with a local modular Hamiltonian there is always a canonical choice for the perturbed thread configurations that exploits bulk locality. To do so, we express the bit thread formalism in terms of differential forms so that it becomes manifestly background independent. We show that the Iyer-Wald formalism provides a natural candidate for a canonical local perturbation, which can be used to recast the problem of metric reconstruction in terms of the inversion of a particular linear differential operator. We examine in detail the inversion problem for the case of spherical regions and give explicit expressions for the inverse operator in this case. Going beyond linear order, we argue that the operator that must be inverted naturally increases in order. However, the inversion can be done recursively at different orders in the perturbation. Finally, we comment on an alternative way of reconstructing the metric non-perturbatively by phrasing the inversion problem as a particular optimization problem.