arXiv subjects

Jorge E. Santos

Publications and source records attributed to Jorge E. Santos.

At least 19 recordsLinked to original sources

arXiv2026

The BTZ black hole, the Third Law and gravitational collapse

We prove that a Third Law of black hole mechanics holds for the BTZ black hole in 3d gravity coupled to matter obeying the dominant energy condition. This law states that initial data containing a trapped surface cannot evolve in finite time to a black hole that coincides with extremal BTZ on the event horizon, for any choice of boundary conditions at infinity. The result is proved by defining a quasilocal energy and angular momentum and using spinorial methods to establish a BPS inequality that is saturated by the extremal BTZ solution. Nevertheless, we show that gravitational collapse of a massless scalar field can result in the formation of an extremal BTZ black hole in finite time. The difference between these results arises because gravitational collapse occurs in the Neveu-Schwarz sector, whereas extremal BTZ is supersymmetric in the Ramond sector. Solutions that settle down to extremal BTZ in infinite time along the event horizon are also discussed.

gr-qc↗

arXiv2026

Black hole spectroscopy: from theory to experiment

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.

gr-qc↗

arXiv2026

Formation of extremal Reissner-Nordström black holes: insights from numerics

An extremal Reissner-Nordström 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 Ansätze. 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 Ansätze. 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 non-zero cosmological constant.

gr-qc↗

arXiv2026

Violation of the third law of black hole mechanics in vacuum gravity

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 pre-existing 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 does not contain a black hole.

gr-qc↗

arXiv2026

Axions Create Singularities on Extremal Horizons

We show that axions cause extremal black holes to have singular horizons. This is true for almost all values of the axion mass and coupling provided the black hole is rotating and has some arbitrarily small nonzero charge. When the axion mass becomes large, these singularities are related to the recently discovered singularities induced by higher-derivative corrections to the Einstein-Maxwell equations. Away from extremality, this effect produces anomalously large tidal forces in the vicinity of near-extremal horizons, causing breakdown of the effective theory.

hep-th↗

arXiv2026

After the Fluid: Subexponential Decay in AdS$_4$

We study the late-time behaviour of nonlinear perturbations of Schwarzschild-AdS$_4$ black branes and show that real-analytic initial data generically enter a regime controlled by the large-$k$ tail of the quasinormal mode spectrum $\{ω_{k\,n}\}$. Using the asymptotic scaling $\mathrm{Im}\,ω_{k\,n} \sim k^{-1/5}$ of the planar AdS$_4$ black brane, we derive a universal prediction that boundary observables decay in a stretched-exponential manner, specifically as $\exp(-c\, t^{5/6})$ up to a mild polynomial prefactor. Fully nonlinear numerical evolutions employing Fourier spectral and discontinuous Galerkin methods confirm this behaviour for small black holes and show consistent scaling - after suppressing long-lived low-$k$ modes - for larger ones. These results indicate that stretched-exponential decay with exponent $5/6$ is a robust feature of AdS$_4$ gravitational dynamics with real-analytic data, arising from geometric-optics physics rather than hydrodynamic modes.

hep-th↗

arXiv2026

When AdS$_3$ Grows Hair: Boson Stars, Black Holes, and Double-Trace Deformations

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 AdS$_3$ 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 $κ< κ_{\rm AdS}$, global AdS$_3$ becomes unstable and we identify its nonlinear endpoint as a zero-frequency boson star with energy below that of AdS$_3$, 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 AdS$_3$ gravity with double-trace deformations.

hep-th↗

arXiv2026

Kerr Black Hole Ringdown in Effective Field Theory

We develop a systematic effective field theory calculation of the quasinormal modes of Kerr black holes valid for arbitrary spin, providing model-independent corrections to their ringdown spectrum directly relevant for gravitational-wave observations. Close to extremality, the effective field theory corrections in the grand-canonical ensemble exhibit an oscillatory dependence on $\log τ_{H}$, with $τ_H \equiv T_H/Ω_H$ a dimensionless measure of the black hole temperature. This behaviour signals an underlying discrete-scale-invariant structure.

gr-qc↗

arXiv2025

Double-trace instability of BTZ black holes

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 $\unicode{x2013}$ previously the only known unstable sector $\unicode{x2013}$ 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 AdS$_3$ 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.

gr-qc↗

arXiv2025

Localised $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathbb{T}^4$ Black Holes

We numerically construct asymptotically global $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ black holes in type IIB supergravity, with $\mathbb{R}_t \times SO(2) \times SO(3) \times U(1)^4$ symmetry, localised on the $\mathrm{S}^3$ and translationally invariant along the torus. These solutions, with horizons whose spatial cross sections have $\mathrm{S}^4 \times \mathbb{T}^4$ topology, dominate the microcanonical ensemble at low energies. At higher energies, a first-order phase transition occurs to $\mathrm{BTZ} \times \mathrm{S}^3 \times \mathbb{T}^4$ black holes $-$ possessing $\mathbb{R}_t \times SO(2) \times SO(4) \times U(1)^4$ symmetry and $\mathrm{S}^1 \times \mathrm{S}^3 \times \mathbb{T}^4$ 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 $\mathrm{CFT}_2$ sparseness bootstrap condition, and shed light on how macroscopic entanglement in thermal phases encodes microscopic structure via internal directions.

hep-th↗

arXiv2025

Frozen Firewall: Generic Singularity Formation on an Extremal Horizon

It is known that linearized perturbations of extremal black holes result in growing curvature on the horizon. However, nonlinear perturbations typically do not evolve to extremal black holes and do not have growing curvature at late times. We show that a large class of nonlinear perturbations of an extremal planar anti-de Sitter black hole does have horizon curvature that grows unbounded in time. The late time behavior of the nonlinear evolution is found to be captured by a linearized analysis. We argue that the generic nonlinear perturbation behaves similarly.

hep-th↗

arXiv2025

The Low Energy Limit of BFSS Quantum Mechanics

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.

hep-th↗

arXiv2025

Localized states of BFSS super quantum mechanics

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.

hep-th↗

arXiv2025

Asymptotically Flat Rotating Topological Stars

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, S$^1\times\mathbb{R}^{1,3}$. 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.

hep-th↗

arXiv2025

Are $S^1\times S^2$ wormholes generic with large sources?

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. This hypothesis can be studied in a context with asymptotically locally AdS$_4$ 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 {\it 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.

hep-th↗

arXiv2025

Constraints are not enough

The Euclidean Einstein-Hilbert action is well-known to be unbounded below and thus to raise many questions regarding the definition of the gravitational path integral. A variety of works since the late 1980's have suggested that this problem disappears when one fixes a foliation of the spacetime and imposes the corresponding gravitational constraints. However, we show here that this approach fails with various classes of boundary conditions imposed on the foliation: compact slices without boundary, asymptotically flat, or asymptotically locally anti-de Sitter slices. We also discuss the idea of fixing the scalar curvature and Wick-rotating the conformal factor, and show that it also fails to produce an action bounded from below.

hep-th↗

arXiv2025

Ill-posedness of the Cauchy problem for linearized gravity in a cavity with conformal boundary conditions

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 $Y_{\ell m}$, and whose coefficient of exponential growth in time goes as $\sim \ell^{1/3}$. We use these modes to construct a sequence of solutions for which the initial data converge to zero as $\ell \rightarrow \infty$ 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.

gr-qc↗

arXiv2025

Tails from the Bulk: Gravitational Decay in AdS$_5$

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.

hep-th↗