Program

A detailed understanding of how two black horizons (in a binary black hole system) merge has been developed over the past decade using analytical and numerical methods.  In this talk I will summarize these results with an emphasis on the geometric aspects of the merger and with applications to gravitational wave astronomy.  In particular,  these results will be applied to estimate the mass and spin of the remnant black hole.

Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However, theoretically, there are many unanswered questions about how black holes come into being and about the structures of the spacetime singularities. In this talk, we will present several results in these directions about black hole formation, about naked singularities, and about cosmic censorship.

TBA

While extensive studies have been conducted on the critical phenomena of gravitational collapse in spherical symmetry, the behavior of such spacetimes when departing from this symmetry remains an active field of research in numerical relativity. A principal challenge in this context is the difficulty of comparing results from different computational programs, which has hindered the ability to reach vetted, confident conclusions. A crucial initial step in this direction was taken in which the `bamps`, `prague`, and `sphGR` codes were employed to simulate the same families of vacuum data. The results were shown to be in excellent agreement. In this talk, we present results from comparative studies conducted with these codes, building upon the initial results and analyzing data families not analyzed in the previous work. Excellent agreement is found for these new results as well. I will also discuss the remaining challenges.

TBA

Title: The moduli space of dynamical spherically symmetric black hole spacetimes and the extremal threshold

Abstract: We study the moduli space of spherically symmetric, asymptotically flat solutions of the Einstein–Maxwell equations coupled to a real scalar field. Near the Reissner–Nordström family, I will present a proof showing that the black hole region is foliated by codimension-one stable manifolds of constant charge-to-mass ratio, and that the black hole formation threshold is exactly the set of asymptotically extremal black holes. This is based on joint work with Y. Angelopoulos (BIMSA) and C. Kehle (MIT).

Title: Extremal black holes are codimension-one in gravitational collapse of a spherical charged scalar field - but away from the threshold of collapse
Abstract: Kehle and Unger have conjectured that extremal black holes form generically at the threshold between solutions that form black holes and solutions that do not. Motivated by this conjecture, we (re)investigate spherical charged scalar field collapse in 3+1 and 4+1 dimensions. We find the expected type-II critical collapse at the threshold of collapse where Q, M, and Q/M of the black hole all go to zero as powers of distance to the threshold. Surprisingly, we also find a codimension-1 surface inside the set of collapsing data, such that Q/M approaches 1 from one side. The mechanism is closely related to the formation of extremal black hole horizons in a toy model of gravitational collapse previously investigated by Murata, Tanahashi and Reall, Gelles and Pretorius, and Kehle and Unger.

This is work in collaboration with Laetitia Martel and Satwik Mittal.

Title: Extremal Black Hole Formation in Charged Scalar Field Collapse, and the Extremal Critical Collapse Conjecture

Abstract: In the spherical Einstein-Maxwell-charged scalar system, Kehle and Unger have constructed characteristic gluing data for the formation of extremal Reissner-Nordström black holes in collapse, thus disproving the "third law of black hole mechanics". We evolve numerical examples of such data, both of the type where the gluing null cone is outgoing and becomes the event horizon, and of the type where the gluing null cone is ingoing and becomes parallel to the Cauchy horizon. This provides the first numerical examples of extremal black hole formation in charged scalar field collapse. All of our solutions contain either trapped surfaces or antitrapped surfaces in the interior of the black hole. We explore how the onset of these surfaces depends on the various parameters of the system.

This is work in collaboration with Maxime Gadioux, Carsten Gundlach, and Laetitia Martel.

There is a compelling analogy between the dynamics of gravitational collapse near the threshold of forming a black hole and a phase transition, with intimate connections to the question of whether one can form naked singularities. In this talk, I will discuss some recent work studying the collapse of a distribution of particles near the threshold for forming a significantly charged black hole. In one part of the phase diagram for this setup, the boundary between solutions that collapse to a black hole and those that do not is characterized by a discontinuous transition where the threshold solutions are stationary (horizonless) charged shells. However, this behavior terminates at a critical point beyond which the threshold solution becomes an extremal black hole. I will illustrate how the timescales governing the dynamics of nearby solutions obey simple scaling relations. These results are related to recent work that disproves the third law of black hole dynamics and suggest a possible route to forming extremal spinning black holes.

Abstract: In this talk, I will discuss the numerical construction of extremal black holes from charged scalar fields. Specifically, I will give numerical evidence that asymptotically extremal black holes act as universal threshold solutions of the Einstein-Maxwell-scalar field system. These threshold solutions can be understood from the perspective of critical phenomena, with horizon instabilities emerging in the appropriate limit. The instabilities persist on the dispersive side of the critical point, generating large curvatures visible from future null infinity and probing the limits of cosmic censorship. I will conclude with a discussion of the formation channels for these objects, including the possibility that they form directly from gravitational collapse.

Based on arXiv:2602.11256.

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.

Extremal black holes have traditionally been regarded as unphysical objects that cannot form through gravitational collapse in astrophysically plausible scenarios, an idea long reinforced by the so-called “third law of black hole thermodynamics”. In the asymptotically flat setting, Kehle and Unger recently provided counterexamples to the third law by constructing regular Cauchy data for the Einstein-Maxwell-charged scalar field system that undergo gravitational collapse to form an exactly extremal Reissner–Nordström black hole in finite time. In this talk, we will explore how these results can be extended to the case Λ>0. Focusing on the Einstein-scalar field system, we will discuss the existence of not only solutions in which an exactly extremal Schwarzschild-de Sitter black hole is formed in finite time, but also of solutions exhibiting dynamical formation of an exactly extremal Schwarzschild-de Sitter white hole and of Nariai in finite time. All these solutions can be regarded, in particular, as counterexamples to the third law without charge.

Small naked singularities—those not shielded by a macroscopic event horizon—are ubiquitous in classical General Relativity. Their existence constitutes apparent violations of the weak cosmic censorship conjecture, which asserts that physically reasonable solutions should appear regular to asymptotic observers. In this talk, we will show how the inclusion of quantum effects resolves these pathologies by uplifting naked singularities into fully regular configurations. Focusing on critical gravitational collapse as a concrete example, we demonstrate that a proper quantum treatment replaces naked singularity formation with black hole formation.

Recently, we have obtained analytic control of the continuously self-similar critical solution for a perfect fluid minimally coupled to gravity by using the number of spacetime dimensions as an expansion parameter. In this talk, I will describe how the critical solution can be constructed systematically in a 1/D expansion, explaining the distinct asymptotic regions that arise and how the sonic point enters as a nonlinear eigenvalue problem that can be solved using asymptotic methods.

Tidal Love numbers provide us a handle to test the nature of compact objects, as well as theories of gravity. There have been several clarifications recently, which makes our understanding of these Love numbers better in the dynamical scenarios. I plan to discuss these recent developments and the recent literature on these issues. I will also highlight some remarkable novel features, for ultra-compact objects as well as for quantum BHs.

In this talk, we'll discuss how to construct a simple scalar that detects initial data sets which give rise to Petrov type D vacuum spacetime developments. As an application, we derive an integral invariant which, when restricted to the appropriate class of asymptotically Euclidean initial data sets, vanishes if and only if the initial dataset is isometric to initial data for the Kerr spacetime. As such, the invariant can be considered a measure of non-Kerrness on such initial data sets. In contrast with other similar invariants constructed through the notion of 'approximate Killing spinors', the present invariant is algebraic in the sense that it is algorithmically computable directly from initial data without having to solve any PDEs on the initial data hypersurface.

A popular strategy for constructing stationary and axisymmetric nonvacuum spacetimes in general relativity is to use Newman–Janis–type algorithms to "spin up" static seed solutions. Such methods are especially appealing when one seeks controlled families of spinning matter configurations, for instance as starting points for studies of spinning gravitational collapse. In this talk, I will revisit an algorithm that can be viewed as a natural culmination of the Newman–Janis trick. We show that it generates only a highly constrained class of spacetimes with an unusually rich symmetry structure: both geodesic motion and scalar-wave propagation are separable, motivating the name "doubly separable" spacetimes. We also identify a degenerate subclass admitting a Killing–Yano tensor, which signals the separability of the Dirac equation. These symmetries, however, come at a cost. We show that doubly separable spacetimes cannot be sourced by massless real scalar fields or perfect fluids, and that electromagnetic fields reduce the class to the Kerr–Newman family. Thus, while Newman–Janis–generated spacetimes provide useful geometries for studying shadows, photon rings, and wave propagation, they do not furnish a general solution-generating technique for physically consistent spinning matter sources.

I discuss critical phenomena in the gravitational collapse of the electromagnetic field in axisymmetry using cylindrical coordinates. The studies involve detailed numerical simulations of four families of dipole and quadrupole initial data fine-tuned to the onset of black formation. Power-law scaling of an electromagnetic field invariant and discrete self-similarity is seen in all cases, with evidence for universality in both features. Comparisons are made with previous results due to Mendoza and Baumgarte, with some remarks made about the differences between the two.

Critical phenomena in gravitational collapse reveal universal features of general relativity near the threshold between dispersion and black hole formation, including discrete self-similarity and power-law scaling. While well understood in spherical symmetry, whether these properties generalize in less symmetric settings remains largely unexplored. In this talk, I present some numerical studies of the collapse of a massless complex scalar field in axisymmetry using a generalized harmonic formulation and the pseudospectral code BAMPS. Both cases with and without angular momentum are being explored. I will discuss how departures from spherical symmetry modify the critical behavior and what role angular momentum plays near the threshold of collapse. Time permitting I will additionally discuss ongoing work with massive fields.

Title: Universality and the Type I / Type II transition in the critical collapse of boson stars.

Abstract: Type I in the collapse of perturbed boson stars in spherical symmetry was first studied by Hawley and Choptuik in 2000, where the critical solution was shown to be an unstable star. Revisiting this setup, and extending it to different self-interacting potentials, we find two locally universal black hole masses for data close to the critical threshold, which do not depend on the type of perturbation used. As expected, but for the first time in this configuration, we also find type II critical collapse, where the critical point is the Choptuik solution. We offer a qualitative description of the transition between types I and II. Given the difference between these two domains, two very different codes were employed for each. Approaching the transition region with both codes further evidences universality and the reproducibility of our results.

We consider a semilinear wave equation with a null-form nonlinearity for maps from R^(1+d) into S^1. For every d ≥ 1, we construct a countable family of discretely self-similar (DSS) blowup solutions and determine their nonlinear stability properties. We show that each profile is stable modulo finitely many un-stable directions, which are identified through an explicit spectral analysis. In particular, the ground state profiles are stable. The proof is based on delicate resolvent estimates for the linearized operator and a nonlinear perturbation argument. This appears to be the first rigorous construction and stability analysis of DSS blowup for a nonlinear wave equation. The talk is based on a joint work with David Hilditch (Lisbon) and David Wallauch (EPFL).

In this talk we will explain the main ideas of relativistic elasticity and give some examples of elastic materials.

I will discuss recent work aimed at analyzing critical collapse with elastic materials. It is well-known that gravitational collapse in perfect fluid models displays emergent continuous self-similarity at the threshold of black hole formation. Such matter models can be extended to include relativistic elasticity effects, and continuous self-similar configurations arise in this context when choosing a scale-invariant elastic matter model. A discrete family of such solutions is determined numerically by solving the associated boundary value problem. I will present results for the fundamental mode and lowest overtones and discuss how the physical properties of these threshold collapsing solutions are affected by elasticity parameters, namely the shear index and the Poisson ratio.

We study the gravitational interaction of very strong pulses of electromagnetic radiation, up to and beyond gravitational collapse. We demonstrate the existence of very compact states close to the threshold of collapse, both for a single pulse, and a head-on collision of such pulses, and we measure their compactness to be above the maximum value proposed by the hoop conjecture.

For a single pulse, above the threshold of collapse a fast black hole is produced. Depending on the amount of tuning, head-on collisions can form two  horizonless states, two small black holes or one big black hole. Our results show that the gravitational interaction of massless fields can lead to nontrivial final or intermediate states, while giving rise to extremely high luminosity and compactness.

TBC