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1. Imprints of phase transitions on Kasner singularities

   https://doi.org/10.1103/PhysRevD.109.126018  

   Caceres, Elena; Shashi, Sanjit; Sun, Hao-Yu (June 2024, Physical Review D)

   Under the $\mathrm{AdS}/\mathrm{CFT}$correspondence, asymptotically anti–de Sitter geometries with backreaction can be viewed as conformal field theory states subject to a renormalization group (RG) flow from an ultraviolet (UV) description toward an infrared (IR) sector. For black holes, however, the IR point is the horizon, so one way to interpret the interior is as an analytic continuation to a “trans-IR” imaginary-energy regime. In this paper, we demonstrate that this analytic continuation preserves some imprints of the UV physics, particularly near its “end point” at the classical singularity. We focus on holographic phase transitions of geometric objects in round black holes. We first assert the consistency of interpreting such black holes, including their interiors, as RG flows by constructing a monotonic $a$function. We then explore how UV phase transitions of entanglement entropy and scalar two-point functions, each of which are encoded by bulk geometry under the holographic mapping, are related to the structure of the near-singularity geometry, which is quantified by Kasner exponents. Using 2D holographic flows triggered by relevant scalar deformations as test beds, we find that the 3D bulk’s near-singularity Kasner exponents can be viewed as functions of the UV physics precisely when the deformation is nonzero. Published by the American Physical Society2024 

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2. Kasner Bounces and Fluctuating Collapse Inside Hairy Black Holes with Charged Matter

   https://doi.org/10.1007/s40818-024-00192-x  

   Li, Warren; Van_de_Moortel, Maxime (June 2025, Annals of PDE)

   Abstract We study the interior of black holes in the presence of charged scalar hair of small amplitude$$\epsilon $$ $ϵ$on the event horizon and show their terminal boundary is a crushing Kasner-like singularity. These spacetimes are spherically symmetric, spatially homogeneous and they differ significantly from the hairy black holes with uncharged matter previously studied in[M. Van de Moortel, Violent nonlinear collapse inside charged hairy black holes, Arch. Rational. Mech. Anal., 248, 89, 2024]in that the electric field is dynamical and subject to the backreaction of charged matter. We prove this charged backreaction causes drastically different dynamics compared to the uncharged case that ultimately impact the formation of the spacelike singularity, exhibiting novel phenomena such asCollapsed oscillations: oscillatory growth of the scalar hair, nonlinearly induced by the collapseAfluctuating collapse: The final Kasner exponents’ dependency in$$\epsilon $$ $ϵ$is via an expression of the form$$|\sin \left( \omega _0 \cdot \epsilon ^{-2}+ O(\log (\epsilon ^{-1}))\right) |$$ $|sin\left({\omega }_0,·,{ϵ}^{-2},+,O,(log\left({ϵ}^{-1}\right))\right)|$.AKasner bounce: a transition from an unstable Kasner metric to a different stable Kasner metricThe Kasner bounce occurring in our spacetime is reminiscent of the celebrated BKL scenario in cosmology. We additionally propose a construction indicating the relevance of the above phenomena – including Kasner bounces – to spacelike singularities inside more general (asymptotically flat) black holes, beyond the hairy case. While our result applies to all values of$$\Lambda \in \mathbb {R}$$ $\Lambda \in R$, in the$$\Lambda <0$$ $\Lambda <0$case, our spacetime corresponds to the interior region of a charged asymptotically Anti-de-Sitter stationary black hole, also known as aholographic superconductorin high-energy physics, and whose exterior region was rigorously constructed in the recent mathematical work [W. Zheng,Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes, arXiv.2410.04758]. 

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3. Dynamics of $E_6$ chiral gauge theories

   https://doi.org/10.1103/cksl-66x7  

   Goh, Andrew; Murayama, Hitoshi; Singh, Gup; Suter, Bethany; Wong, Jason (August 2025, Physical Review D)

   We present exact nonperturbative vacuum solutions to chiral gauge theories based on the $E_6$gauge group and several matter fermions in the fundamental $27$-dimensional representation. They are obtained when supersymmetric versions are perturbed by small supersymmetry breaking by anomaly mediation. The universality classes obtained are very different from what can be conjectured by the tumbling hypothesis. In particular, the case with three $27\mathrm{s}$may have an unbroken SU(3) symmetry with massless composite fermions in $10$of SU(3). For this case, we employed numerical techniques to obtain the exact ground state. 

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4. Pseudo-easy-axis anisotropy in antiferromagnetic $S=1$ diamond-lattice systems

   https://doi.org/10.1103/PhysRevB.110.174438  

   Vaidya, S; Hernández-Melián, A; Tidey, J P; Curley, S_P M; Sharma, S; Manuel, P; Wang, C; Hannaford, G L; Blundell, S J; Manson, Z E; et al (November 2024, Physical Review B)

   We investigate the magnetic properties of $S=1$antiferromagnetic diamond-lattice, $\mathrm{Ni}{X}_2{\left(\mathrm{pyrimidine}\right)}_2$ $(X=\mathrm{Cl}, \mathrm{Br})$, hosting a single-ion anisotropy (SIA) orientation which alternates between neighboring sites. Through neutron diffraction measurements of the $X=\mathrm{Cl}$compound, the ordered state spins are found to align collinearly along a pseudo-easy axis, a unique direction created by the intersection of two easy planes. Similarities in the magnetization, exhibiting spin-flop transitions, and the magnetic susceptibility in the two compounds imply that the same magnetic structure and a pseudo-easy axis is also present for $X=\mathrm{Br}$. We estimate the Hamiltonian parameters by combining analytical calculations and Monte Carlo (MC) simulations of the spin-flop and saturation field. The MC simulations also reveal that the spin-flop transition occurs when the applied field is parallel to the pseudo-easy axis. Contrary to conventional easy-axis systems, there exist field directions perpendicular to the pseudo-easy axis for which the magnetic saturation is approached asymptotically and no symmetry-breaking phase transition is observed at finite fields. Published by the American Physical Society2024 

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5. Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

   https://doi.org/10.1007/s00205-023-01842-3  

   Coti Zelati, Michele; Elgindi, Tarek M.; Widmayer, Klaus (February 2023, Archive for Rational Mechanics and Analysis)

   Abstract We study the behavior of solutions to the incompressible 2dEuler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier–Stokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus$$\mathbb {T}^2$$ $T^2$in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an “inviscid damping” mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on$$\mathbb {T}^2$$ $T^2$. Our construction of the new stationary states builds on a degeneracy in the global structure of the Kolmogorov flow on$$\mathbb {T}^2$$ $T^2$, and we also show a lack of correspondence between the linearized description of the set of steady states and its true nonlinear structure. Both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel are very different. We show that the only stationary states near them must indeed be shears, even in relatively low regularity. In addition, we show that this behavior is mirrored closely in the related Navier–Stokes settings: the linearized problems near the Poiseuille and Kolmogorov flows both exhibit an enhanced rate of dissipation. Previous work by us and others shows that this effect survives in the full, nonlinear problem near the Poiseuille flow and near the Kolmogorov flow on rectangular tori, provided that the perturbations lie below a certain threshold. However, we show here that the corresponding result cannot hold near the Kolmogorov flow on$${\mathbb T}^2$$ $T^2$. 

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