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1. Note on black holes with kilometer-scale ultraviolet regulators

   https://doi.org/10.1088/1361-6382/ad5e57  

   Boos, Jens; Carone, Christopher_D (July 2024, Classical and Quantum Gravity)

   Abstract Regular black hole metrics involve a universal, mass-independent regulator that can be up to $O\left(700\text{km}\right)$while remaining consistent with terrestrial tests of Newtonian gravity and astrophysical tests of general relativistic orbits. However, for such large values of the regulator scale, the metric describes a compact, astrophysical-mass object with no horizon rather than a black hole. We note that allowing the regulator to have a nontrivial mass dependence preserves the horizon, while allowing large, percent-level effects in black hole observables. By considering the deflection angle of light and the black hole shadow, we demonstrate this possibility explicitly. 

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2. Stability and Instability of Self-Gravitating Relativistic Matter Distributions

   https://doi.org/10.1007/s00205-021-01647-2  

   Hadžić, Mahir; Lin, Zhiwu; Rein, Gerhard (May 2021, Archive for Rational Mechanics and Analysis)

   Abstract We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein–Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein–Euler system, i.e., relativistic models of stars. Such steady states are embedded into one-parameter families parameterized by their central redshift$$\kappa >0$$ $\kappa >0$. We prove their linear instability when$$\kappa $$ $\kappa$is sufficiently large, i.e., when they are strongly relativistic, and prove that the instability is driven by a growing mode. Our work confirms the scenario of dynamic instability proposed in the 1960s by Zel’dovich & Podurets (for the Einstein–Vlasov system) and by Harrison, Thorne, Wakano, & Wheeler (for the Einstein–Euler system). Our results are in sharp contrast to the corresponding non-relativistic, Newtonian setting. We carry out a careful analysis of the linearized dynamics around the above steady states and prove an exponential trichotomy result and the corresponding index theorems for the stable/unstable invariant spaces. Finally, in the case of the Einstein–Euler system we prove a rigorous version of the turning point principle which relates the stability of steady states along the one-parameter family to the winding points of the so-called mass-radius curve. 

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3. Stars Crushed by Black Holes. II. A Physical Model of Adiabatic Compression and Shock Formation in Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac3fb9  

   Coughlin, Eric R.; Nixon, C. J. (February 2022, The Astrophysical Journal)

   Abstract We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,r_p, is well within the tidal radius of the black hole,r_t, i.e., whenβ≡r_t/r_p≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted ${\rho }_{\max }\propto {\beta }^3$and $T_{\max }\propto {\beta }^2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings ${\rho }_{\max }\propto {\beta }^{1.62}$and $T_{\max }\propto {\beta }^{1.12}$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter of the star nears the direct capture radius, atβ∼ 12.5 (2.7) for a solar-like star disrupted by a 10⁶M_⊙(10⁷M_⊙) supermassive black hole. 

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4. Tip of the Iceberg: Overmassive Black Holes at 4 < z < 7 Found by JWST Are Not Inconsistent with the Local $M_{\mathrm{BH}}-M_{\star }$ Relation

   https://doi.org/10.3847/1538-4357/ada603  

   Li, Junyao; Silverman, John D; Shen, Yue; Volonteri, Marta; Jahnke, Knud; Zhuang, Ming-Yang; Scoggins, Matthew T; Ding, Xuheng; Harikane, Yuichi; Onoue, Masafusa; et al (February 2025, The Astrophysical Journal)

   Abstract JWST is revealing a remarkable new population of high-redshift (z ≳ 4), low-luminosity active galactic nuclei in deep surveys and detecting the host galaxy's stellar light in the most luminous and massive quasars atz ∼ 6 for the first time. Recent findings claim that supermassive black holes (SMBHs) in these systems are significantly more massive than predicted by the local black hole (BH) mass–stellar mass ( ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$) relation and that this is not due to sample selection effects. Through detailed statistical modeling, we demonstrate that the coupled effects of selection biases (i.e., finite detection limit and requirements for detecting broad lines) and measurement uncertainties can largely explain the reported offset and flattening in the observed ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation toward the upper envelope of the local relation, even for those at ${\mathcal{M}}_{\mathrm{BH}}<10^8{M}_{\odot }$. We further investigate the possible evolution of the ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation atz ≳ 4 with careful treatment of observational biases and consideration of the degeneracy between intrinsic evolution and dispersion in this relation. The bias-corrected intrinsic ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation in the low-mass regime ( ${\mathcal{M}}_{\star }\lesssim 10^{10}{M}_{\odot }$) suggests a large population of low-mass BHs ( ${\mathcal{M}}_{\mathrm{BH}}\lesssim 10^5{M}_{\odot }$), possibly originating from lighter seeds, may remain undetected or unidentified. These results underscore the importance of forward modeling observational biases to better understand BH seeding and SMBH–galaxy coevolution mechanisms in the early universe, even with the deepest JWST surveys. 

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5. Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile

   https://doi.org/10.1007/s00454-022-00426-4  

   Greenfeld, Rachel; Tao, Terence (January 2023, Discrete & Computational Geometry)

   Abstract We construct an example of a group$$G = \mathbb {Z}^2 \times G_0$$ $G=Z^2\times G_0$for a finite abelian group $$G_0$$ $G_0$, a subsetEof $$G_0$$ $G_0$, and two finite subsets$$F_1,F_2$$ $F_1,F_2$of G, such that it is undecidable in ZFC whether$$\mathbb {Z}^2\times E$$ $Z^2\times E$can be tiled by translations of$$F_1,F_2$$ $F_1,F_2$. In particular, this implies that this tiling problem isaperiodic, in the sense that (in the standard universe of ZFC) there exist translational tilings ofEby the tiles$$F_1,F_2$$ $F_1,F_2$, but no periodic tilings. Previously, such aperiodic or undecidable translational tilings were only constructed for sets of eleven or more tiles (mostly in $$\mathbb {Z}^2$$ $Z^2$). A similar construction also applies for$$G=\mathbb {Z}^d$$ $G=Z^d$for sufficiently large d. If one allows the group$$G_0$$ $G_0$to be non-abelian, a variant of the construction produces an undecidable translational tiling with only one tile F. The argument proceeds by first observing that a single tiling equation is able to encode an arbitrary system of tiling equations, which in turn can encode an arbitrary system of certain functional equations once one has two or more tiles. In particular, one can use two tiles to encode tiling problems for an arbitrary number of tiles. 

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