Schedule for: 22w5025 - At the Interface of Mathematical Relativity and Astrophysics

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

In this talk based on recent work with Thomas Bäckdahl, Pieter Blue and Siyan Ma, I will review some aspects of our approach to the black hole stability problem. The use of a radiation gauge plays an important role and I will discuss some features of the resulting reduced system.

The Teukolsky master equations are a family of PDEs describing the linear behavior of perturbations of the Kerr black hole family, of which the wave equation is a particular case. As a first essential step towards stability, Whiting showed in 1989 that the Teukolsky equation on subextremal Kerr admits no exponentially growing modes.  

We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the PDC front desk for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

The LIGO and Virgo interferometers have detected nearly 100 binary black hole mergers to date. The black holes formed by these mergers have provided our first opportunity to directly observe quasi-normal modes (QNMs) emitted by a perturbed Kerr black hole. However, detecting more than the dominant QNM is challenging. It has been claimed that an overtone of the dominant QNM can be detected at the merger of GW150914 (and other events); the detection of a sub-dominant angular mode has been claimed in the merger GW190521. Both of these claims remain controversial, with conflicting evidence presented by different groups. I will review these detection claims and the evidence for each.

Black hole spectroscopy is as a powerful approach to extract spacetime information from gravitational wave observed signals. However, quasinormal mode (QNM) spectral instability under high wave-number perturbations has been recently shown to be a common classical general relativistic phenomenon. I will discuss these recent results on the stability of QNM in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis.

There are two important physical processes around black holes that can be well described using relativistic perturbation theory: Scattering of electromagnetic and gravitational waves (and other fields) and quasinormal mode oscillations that take place, for instance, after the coalescence of a black hole binary. It is well-known that these physical processes can be described in terms of  gauge-invariant master functions. We have analyzed the space of all the possible master functions for the case of non-rotating black holes and we find two branches of solutions. One branch includes the known results: In the odd-parity case, the most general master function is an arbitrary linear combination of the Regge-Wheeler and the Cunningham-Price-Moncrief master functions whereas in the even-parity case it is an arbitrary linear combination of the Zerilli master function and another master function that is new to our knowledge. The other branch is very different since it includes an infinite collection of potentials which in turn lead to an independent collection master of functions which depend on the potential.  We also find that of all them are connected via Darboux transformations. These transformations preserve physical quantities like the quasinormal mode frequencies and the infinite hierarchy of Korteweg-de Vries conserved quantities, revealing a new hidden symmetry in the description of the perturbations of Schwarzschild black holes: Darboux covariance.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Members of the discussion panel: E. Gasperin (chair) A. Bernal A. Vaño-Viñuales Celia Escamilla

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modelled by non-expanding horizons (NEHs). Multipole moments to characterize their geometry will be introduced. A 1-dimensional extension of the BMS group acts on NEH. These symmetries will be used to define charges and fluxes on NHEs, as well as perturbed NEHs (gravitational radiation). They have physically attractive properties. Also, a new quadrupole formula for gravitational radiation through the cosmological horizon in de Sitter spacetime will be presented.

A pseudospectrum analysis has recently provided evidence of a potential generic instability of the black hole (BH) quasinormal mode (QNM) spectrum. Such instability analysis depends on the assessment of the size of the perturbations. This is encoded in the scalar product and its choice is not unique. In this talk, we will address the impact of the scalar product choice, founding it on the physical energy scales of the problem. Applications of the scalar product in the QNM problem will be discussed as well as further insights into potentially geometric structures in the QNM problem brought to the forefront by geometric structures in the QNM problem brought to the forefront by the expression for the energy flux at null infinity.

Asymptotic symmetries play an important role and have deep implications in our understanding of gravity. After a short review of asymptotic symmetries at null infinity in Einstein gravity, I will introduce the Weyl-BMS group, a recent extension of the original BMS group, and discuss its main properties. I will also show that the asymptotic Einstein’s equations can be derived from the requirement that the Noether charges associated to the Weyl-BMS generators form a representation of the Weyl-BMS algebra.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

Gravity manifests itself as curvature of spacetime, and its strength can be measured by considering the variations of radius, area and volume of small balls with respect to their counterparts in flat spacetime. These variations can actually be put in relation, via the Einstein field equations, with the energy density of matter at the ball's centre. In this talk I will also consider what happens when the matter energy density vanishes. The elementary geometric quantities still feel the effect of pure gravity, leading to variations that should be related to the gravitational strength or, in simple words, to the gravitational energy density. These variations now involve terms quadratic in the curvature that can be appropriately put in connection with the Bel-Robinson tensor. New definitions of quasi-local gravitational energy arise. Some basic examples will be discussed.

Apparent horizons are routinely used in numerical relativity to infer properties of black holes in simulations of dynamical systems. Advances in numerical methods allowed us to follow these objects into the interior of merging black holes, revealing how the two original horizons connect (non-smoothly) with the remnant horizon. However, this still left the question of their final fate open. In this talk, I will present our most recent results on axisymmetric head-on mergers, showing that the evolution of apparent horizons is much more intricate than previously thought: In the interior of the newly formed common horizon, the original horizons are individually annihilated by unstable horizon-like structures. This completes our picture of how two black holes become one and provides the analog of the famous pair-of-pants diagram of the event horizon now for the apparent horizon.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

E Gasperin (chair) JA Valiente Kroon Claudia Moreno Nestor Ortiz Tonatiuh Matos

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Understanding the behavior of black hole relaxation to equilibrium is presenting new challenges at theoretical and practical levels. This talk will discuss some recent developments which are raising new (and revisiting old) questions on this topic.

Before the first successful numerical simulations of binary black hole mergers in 2005, it was considered plausible that the gravitational wave signal could have complicated modulations and even be chaotic. After all, general relativity is a non-linear theory and these non-linearities are especially important near the merger. However, the reality is that the signals are so far seen to be rather simple. This does not mean that the signals are trivial, rather that the complications due to e.g. precession, eccentricity etc. are contained in the deviations from a simple underlying model. In this talk, we will propose a reason for this simplicity based on the framework of "singularity theory" developed by Whitney, Arnold and Thom in the 1960s. We shall propose that certain radiative aspects of binary black hole mergers are similar to other common observed physical phenomena such as caustics and rainbows in optics, and this theory provides hints for deeper mathematical structures in binary black hole dynamics. This is a joint talk by JL Jaramillo and B. Krishnan.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.

When black holes merge (or form by gravitational collapse), we have a common dynamical horizon whose geometry changes dramatically as it settles down to the final Kerr horizon. This evolution can be invariantly characterized by the dynamics of a set of multipoles. Unfortunately, the causal structure of space-time prevents the outside observers from directly witnessing it. However, thanks to Einstein’s equations, this dynamics is encoded in the profiles of gravitational waves observed at infinity. Using results presented in previous talks at this workshop, and from joint work with Neev Khera, I will present a transform that reconstructs the late time dynamics of the horizon geometry using gravitational waves at null infinity. Just as one monitors changes in the internal structure of objects from outside using electromagnetic tomography, one can image the horizon dynamics using gravitational waves at infinity.