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1. Extremal black holes that are not extremal: maximal warm holes

   https://doi.org/10.1007/JHEP01(2022)064  

   Dias, Óscar J.; Horowitz, Gary T.; Santos, Jorge E. (January 2022, Journal of High Energy Physics)

   A bstract We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed. 

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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. Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

   https://doi.org/10.1007/JHEP10(2020)102  

   Hartnoll, Sean A.; Horowitz, Gary T.; Kruthoff, Jorrit; Santos, Jorge E. (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes — for example Reissner- Nordström-AdS — can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit. 

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4. Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity

   https://doi.org/10.1103/PhysRevD.111.024061  

   Nee, Peter James; Lara, Guillermo; Pfeiffer, Harald P; Vu, Nils L (January 2025, Physical Review D)

   Recent efforts to numerically simulate compact objects in alternative theories of gravity have largely focused on the time-evolution equations. Another critical aspect is the construction of constraint-satisfying initial data with precise control over the properties of the systems under consideration. Here, we augment the extended conformal thin sandwich framework to construct quasistationary initial data for black hole systems in scalar Gauss-Bonnet theory and numerically implement it in the open-source p code. Despite the resulting elliptic system being singular at black hole horizons, we demonstrate how to construct numerical solutions that extend smoothly across the horizon. We obtain quasistationary scalar hair configurations in the test-field limit for black holes with linear/angular momentum as well as for black hole binaries. For isolated black holes, we explicitly show that the scalar profile obtained is stationary by evolving the system in time and compare against previous formulations of scalar Gauss-Bonnet initial data. In the case of the binary, we find that the scalar hair near the black holes can be markedly altered by the presence of the other black hole. The initial data constructed here enable targeted simulations in scalar Gauss-Bonnet simulations with reduced initial transients. Published by the American Physical Society2025 

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5. Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

   https://doi.org/10.1088/1475-7516/2022/01/032  

   Hui, Lam; Joyce, Austin; Penco, Riccardo; Santoni, Luca; Solomon, Adam R. (January 2022, Journal of Cosmology and Astroparticle Physics)

   Abstract It is well known that asymptotically flat black holes in generalrelativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governingstatic (spin 0,1,2)perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions,and derive their general properties: (1) solutions that decay withradius spontaneously break the symmetries, and mustdiverge at the horizon;(2) solutions regular at the horizon respect the symmetries, andtake the form of a finite polynomial that grows with radius.Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probesthe worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved. 

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