Euclidean path integrals can be used to prepare states of a Lorentzian QFT. So long as any sources are turned off on the t = 0 surface, the resulting Lorentzian states all belong to the same Hilbert space. Constructing more states than allowed by the Lorentzian density of states means that the resulting states must be linearly dependent. For large amplitude sources and a fixed cutoff on energy, the AdS bulk dual of this effect has been conjectured to be captured by spacetime wormholes. Wormholes should then be generic in the presence of large such Euclidean sources; i.e., at large source amplitude one should find wormholes unless the source is fine-tuned in some way. This hypothesis can be studied in a context with asymptotically locally AdS4 boundaries of topology S1 × S2 in which the wormhole is supported by a source for minimally-coupled massless bulk scalars. In preparation for a later more complete study, we consider here a preliminary toy version of the model in which the spacetimes are cohomogeneity-1, but with the consequence that the sources do not vanish at t = 0. We then find that generic sources at large masses do not lead to wormholes. Along the way we map out the phase diagram for wormhole, thermal AdS, and black hole phases of our cohomogeneity-1 ansatz. We also numerically evaluate their stability by identifying negative modes. In parallel with the previously-studied case of S3 boundaries, the results are analogous to those associated with the familiar Hawking-Page transition.

We perform a comprehensive study of the linear stability of rotating BTZ black holes under massive scalar field perturbations with double-trace boundary conditions. While BTZ black holes are stable under standard Dirichlet and Neumann boundary conditions, we demonstrate that they can develop instabilities when subjected to double-trace boundary conditions. Our key findings are threefold. First, we show that BTZ black holes exhibit instabilities not only for non-axisymmetric modes-previously the only known unstable sector-but crucially also for axisymmetric modes. Second, we prove that the axisymmetric instability is the dominant and most fundamental: configurations unstable to any non-axisymmetric mode are already unstable to the axisymmetric one. Third, we identify regions in the BTZ parameter space where these black holes are unstable while global AdS3 remains stable, and we map the complete onset curves that determine the corresponding stability boundaries. Unlike conventional superradiant instabilities, the BTZ double-trace instability occurs for angular velocities always satisfying the Hawking-Reall bound. We trace the physical origin of these instabilities to the influx of energy and angular momentum through the asymptotic boundary permitted by double-trace deformations for a particular sign of the coupling, rather than to near-horizon effects. Our results provide a prototype for understanding double-trace instabilities in higher-dimensional rotating AdS black holes and suggest the existence of rotating hairy black hole solutions with scalar condensates, which we construct in a companion paper.

A bstract We analyze the recently discovered localized and non-uniform phases of the Banks-Fischler-Shenker-Susskind (BFSS) matrix quantum mechanics. Building on [1], we provide first-principles derivations of their properties and extend the results with new analytic and numerical insights. We show that strongly coupled BFSS dynamics emerge from a specific Carrollian transformation of 11-dimensional supergravity, which we justify in detail. In this framework, the uniform BFSS phase corresponds to a black string in a pp -wave background. We demonstrate that this background is unstable to a Gregory-Laflamme instability and, for the first time, compute the associated growth rate. The instability gives rise to non-uniform and localized phases that dominate the microcanonical ensemble in certain low-energy regimes, with the localized phase also prevailing in the canonical ensemble at low temperatures. We identify the corresponding first- and second-order phase transitions and derive analytic formulas for the thermodynamics of the localized phase, accurate to better than 0 . 3% against numerical results.

An extremal Reissner-Nordstr & ouml;m black hole can form in finite time in the gravitational collapse of a massless charged scalar field. The proof of this is based on the method of characteristic gluing, which involves making an Ansatz for the scalar field at the horizon. We perform a numerical investigation of the characteristic gluing procedure for several different Ans & auml;tze. In each case, gluing is possible only if the final black hole mass is large enough. We find that the minimum required mass varies significantly for different Ans & auml;tze. We also consider the effect of including a mass term for the scalar field. In this case, for each Ansatz we determine the maximum mass-to-charge ratio for the scalar field such that gluing is possible. Analogous results are obtained for a nonzero cosmological constant.

We analyse three-dimensional Einstein gravity coupled to a massive complex scalar field with double-trace boundary conditions. Using high-precision spectral methods, we construct regular AdS3 boson stars together with axisymmetric and non-axisymmetric hairy black holes. For each azimuthal number m, the hairy black holes bifurcate from the BTZ family at the corresponding double-trace instability onset. When the double-trace parameter satisfies κ < κAdS, global AdS3 becomes unstable and we identify its nonlinear endpoint as a zero-frequency boson star with energy below that of AdS3, thereby providing the true ground state of the theory. In the microcanonical ensemble, hairy black holes always carry greater entropy than BTZ at fixed mass and angular momentum, and thus dominate whenever they exist. With notable exceptions, typically hairy black holes do not dominate the canonical nor the grand-canonical ensembles. We further show that, in the singular extremal limit, axisymmetric black holes saturate a generalised minimum-energy theorem under double-trace boundary conditions. These results yield the full nonlinear phase diagram of AdS3 gravity with double-trace deformations.

We study gravitational perturbations of Schwarzschild-AdS black holes in d = 5 and identify a regime of late-time power-law decay for smooth initial data. Based on an analysis of the quasinormal mode spectrum, we predict and characterise this decay behaviour. We perform fully nonlinear numerical evolutions with long integration times that support the prediction and exhibit no signs of instability. Remarkably, the decay is modulated by a universal oscillatory pattern, consistent with subleading corrections from a large-angular-momentum (eikonal) analysis of the quasinormal mode spectrum.

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

Abstract We construct a new class of smooth, horizonless, non-supersymmetric solutions in five-dimensional minimal supergravity, which we call rotating topological stars. Built from a Kerr-Taub-bolt geometry embedded in five dimensions, they constitute the first rotating generalization of the topological star compatible with both smoothness in the interior and standard Kaluza-Klein asymptotics, S1 × ℝ1,3. The solutions carry angular momentum, magnetic and electric charges, and form a discrete tower of states labeled by a primary quantum number controlling the spin. Remarkably, despite lying outside the black-hole extremality bound, they can approach arbitrarily closely (in conserved charges) the Kerr black string with a large boost along the fifth dimension, making them relevant prototypes for rotating and astrophysical black-hole microstates. We analyze their geometry in detail, including their gravitational multipoles that can significantly deviate from those of black holes and the presence of an ergoregion, and show that both geodesics and scalar perturbations separate, paving the way for analyzing their dynamics in future work.

Euclidean path integrals can be used to prepare states of a Lorentzian QFT. So long as any sources are turned off on the t = 0 surface, the resulting Lorentzian states all belong to the same Hilbert space. Constructing more states than allowed by the Lorentzian density of states means that the resulting states must be linearly dependent. For large amplitude sources and a fixed cutoff on energy, the AdS bulk dual of this effect has been conjectured to be captured by spacetime wormholes. Wormholes should then be generic in the presence of large such Euclidean sources; i.e., at large source amplitude one should find wormholes unless the source is fine-tuned in some way.This hypothesis can be studied in a context with asymptotically locally AdS4 boundaries of topology S 1 & times; S 2 in which the wormhole is supported by a source for minimally-coupled massless bulk scalars. In preparation for a later more complete study, we consider here a preliminary toy version of the model in which the spacetimes are cohomogeneity-1, but with the consequence that the sources do not vanish at t = 0. We then find that generic sources at large masses do not lead to wormholes. Along the way we map out the phase diagram for wormhole, thermal AdS, and black hole phases of our cohomogeneity-1 ansatz. We also numerically evaluate their stability by identifying negative modes. In parallel with the previously-studied case of S 3 boundaries, the results are analogous to those associated with the familiar Hawking-Page transition.

We demonstrate numerically the existence of solutions of five-dimensional vacuum gravity describing the formation, in finite time, of an extremal rotating black hole from a preexisting Schwarzschild black hole. This is the first example of a violation of the third law of black hole mechanics in vacuum gravity and demonstrates that the third law is false independently of any matter model. We also demonstrate the existence of solutions describing the formation, in finite time, of an extremal rotating black hole from vacuum initial data that do not contain a black hole.

We numerically construct asymptotically global AdS_3 ×S^3 ×𝕋^4 black holes in type IIB supergravity, with ℝ_t × SO(2) × SO(3) × U(1)^4 symmetry, localised on the S^3 and translationally invariant along the torus. These solutions, with horizons whose spatial cross sections have S^4 ×𝕋^4 topology, dominate the microcanonical ensemble at low energies. At higher energies, a first-order phase transition occurs to BTZ×S^3 ×𝕋^4 black holes - possessing ℝ_t × SO(2) × SO(4) × U(1)^4 symmetry and S^1 ×S^3 ×𝕋^4 horizon topology. By the AdS/CFT correspondence, this transition reflects the spontaneous breaking of the SO(4) R-symmetry of the D1-D5 CFT_2 to SO(3). We also compute the expectation value of the scalar operator with lowest conformal dimension in the low-energy phase. Our SO(3)-localised black holes - together with the U(1)^2-localised solutions of [1] - point to a rich landscape of novel black holes that may approach the CFT_2 sparseness bootstrap condition, and shed light on how macroscopic entanglement in thermal phases encodes microscopic structure via internal directions.

We study the impact of higher-derivative corrections from Effective Field Theory on the quasinormal mode spectrum of Reissner-Nordström black holes. While previous work has explored corrections to Schwarzschild and Kerr black holes — typically using small-rotation approximations — a comprehensive analysis near extremality remains lacking. We focus on Reissner-Nordström black holes as a tractable model admitting an extremal limit, enabling investigation of the effect of these corrections on the so-called zero-damped modes, which dominate in this regime. Specifically, we derive a corrected Moncrief equation governing quasinormal modes and present both analytic and numerical results for the corrected frequencies. This work also offers the first explicit test of the recently proposed “Quasinormal Mode Causality” bound Eur. Phys. J. Plus 139 (2024) 725, which constrains Effective Field Theory coefficients by requiring that quasinormal mode lifetimes do not increase measurably under ultraviolet — complete Effective Field Theory corrections. Using Standard Model contributions — particularly those arising from integrating out the electron — we verify that this bound holds. Our results provide new insights into the interplay between Effective Field Theory, extremal black hole dynamics, and causality in gravitational theories.

Using a mix of analytical and numerical methods, we construct new rotating, charged “hairy” black hole solutions of D = 5, 𝒩 = 8 gauged supergravity that are dual, via the AdS/CFT correspondence, to thermal states in D = 4, 𝒩 = 4 SYM at finite chemical and angular potential, thereby complementing and extending the results of [1–3]. These solutions uplift to asymptotically AdS5 × S5 solutions of Type IIB supergravity with equal angular momenta along AdS5 (J = J1 = J2) and S5 (Q = Q1 = Q2 = Q3). As we lower the mass E at fixed Q and J, the known Cvetič-Lü-Pope (CLP) black holes are unstable to scalar condensation and the hairy black holes constructed here emerge as novel solutions associated to the instability. In the region of phase space where the CLP and hairy black holes coexist, the hairy black holes dominate the microcanonical ensemble and, therefore, describe a new thermodynamic phase of SYM. The hairy black holes extend beyond the CLP extremality surface all the way to the BPS surface, defined by E = 3Q + 2J/L. Through a combination of analytical and numerical techniques, we argue that the BPS limit of the hairy black holes is a singular, horizonless solution, and not a new two-parameter family of BPS black holes that extend the known one-parameter Gutowski-Reall (GR) black hole solution, in contradiction with the conjectures of [1, 2]. To further support our conclusions, we perform a near-horizon analysis of the BPS equations and argue that they do not admit any regular solutions with an horizon.

We construct the first binary black hole solutions of Einstein-Maxwell theory in asymptotically anti-de Sitter space. The attractive force between the two black holes is balanced by the addition of a background electric field, sourced at the conformal boundary. There is a continuous family of bulk solutions for a given boundary profile and temperature, suggesting there is continuous nonuniqueness. We investigate the charges of the solutions and numerically verify that they satisfy a first law of black hole mechanics relation.

We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static empty cavity whose boundary has spherical spatial geometry. It has been recently shown that there exist dynamical instabilities, whose angular dependence is given in terms of spherical harmonics Y_ℓ m, and whose coefficient of exponential growth in time goes as ∼ℓ^1/3. We use these modes to construct a sequence of solutions for which the initial data converge to zero as ℓ→∞ but for which the solution itself does not converge to zero. This implies a lack of continuity of solutions on initial data, which shows that the initial value problem with these boundary conditions is not well-posed. This is in tension with recent mathematical work on well-posedness for such boundary conditions.

We investigate the low energy regime of BFSS quantum mechanics using its holographic dual. We identify three distinct thermodynamic phases (black holes) and analyze their thermodynamic properties extensively, including phase transitions amongst the several phases. While the properties of the canonical ensemble aligns with existing conjectures on BFSS thermodynamics, we uncover intriguing and unexpected behavior in the microcanonical ensemble. Specifically, for sufficiently low energies, we observe the dominance of the localized phase. Surprisingly, we also identify an energy range where the non-uniform phase becomes dominant. The transition between these phases is mediated by a Kol-type topology-changing phenomenon.

Abstract We show that the general charged, rotating black hole in five-dimensional Einstein-Maxwell theory has a singular extremal limit. Only the known analytic solutions with exactly zero charge or zero angular momenta have smooth extremal horizons. We also consider general black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, and show that they also have singular extremal limits except for one special value of the coefficient of the Chern-Simons term (the one fixed by supergravity). Combining this with earlier results showing that extremal black holes have singular horizons in four-dimensional general relativity with small higher derivative corrections, and in anti-de Sitter space with perturbed boundary conditions, one sees that smooth extremal horizons are indeed the exception and not the rule.

Using a mix of analytical and numerical methods, we construct new rotating, charged "hairy" black hole solutions of D=5, N=8 gauged supergravity that are dual, via the AdS/CFT correspondence, to thermal states in D=4, N=4 SYM at finite chemical and angular potential, thereby complementing and extending the results of [arXiv:1005.1287, arXiv:1806.01849, arXiv:1809.04084]. These solutions uplift to asymptotically AdS_5 × S^5 solutions of Type IIB supergravity with equal angular momenta along AdS_5 (J=J_1=J_2) and S^5 (Q=Q_1=Q_2=Q_3). As we lower the mass E at fixed Q and J, the known Cvetič-Lü-Pope (CLP) black holes are unstable to scalar condensation and the hairy black holes constructed here emerge as novel solutions associated to the instability. In the region of phase space where the CLP and hairy black holes coexist, the hairy black holes dominate the microcanonical ensemble and, therefore, describe a new thermodynamic phase of SYM. The hairy black holes extend beyond the CLP extremality surface all the way to the BPS surface, defined by E = 3 Q + 2 J / L. Through a combination of analytical and numerical techniques, we argue that the BPS limit of the hairy black holes is a singular, horizonless solution, and not a new two-parameter family of BPS black holes that extend the known one-parameter Gutowski-Reall (GR) black hole solution, in contradiction with the conjectures of [arXiv:1005.1287, arXiv:1806.01849]. To further support our conclusions, we perform a near-horizon analysis of the BPS equations and argue that they do not admit any regular solutions with an horizon.

Plasma position reflectometry (PPR) will be used for measuring the plasma position and shape in DEMO. To ensure the reliability, PPR systems are optimized for the expected range of plasmas foreseen during the operation. The study and optimization of PPR systems is a highly demanding computational task and the current approach to define the simulation setup and process the simulation results is time-consuming and does not allow the study of a large number of configurations in useful time. In this article we automate the simulation process required for studying and optimizing PPR systems with the REFMUL family of full-wave FDTD codes. A general overview of the fundamental concepts of PPR systems is presented in the context of reflectometry simulations. Different solutions are proposed to produce realistic reflectometer models from CAD files, realistic plasma models, minimize the complexity of the input definition, manage the simulations in HPCs and analyze the simulation results of PPR systems. A new algorithm based in the In-phase and Quadrature (I/Q) detection scheme is developed to extract the phase derivative and the detected signal amplitude from the synthetic signals of a generic simulation. These techniques allow a brute-force approach to reflectometry problems, being essential for the study of reflectometry systems. The algorithms are validated using the 2017 DEMO baseline scenario to test more than 100 different reflectometers at different poloidal positions in the same toroidal section. The application of our methodology can be extended to different reflectometry techniques and other fields. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons .org /licenses /by-nc /4 .0/).

We numerically construct stationary, rotating black binaries in general relativity with a positive cosmological constant. We consider identical black holes with either aligned or anti-aligned spins. Both cases have less entropy than the corresponding single Kerr-Schwarzschild-de Sitter black hole with the same total angular momentum and cosmological horizon entropy. Our solutions establish continuous nonuniqueness in general relativity without matter. They also provide initial data for the spinning binary merger problem (when orbital angular momentum is added).