Peeling the
gravitational onion

Killing tensors are important hidden symmetries that stand behind integrability of geodesic motion and separability of various test field equations in curved spacetimes. In this talk, I will discuss two ways how to generate toy examples of spacetimes with higher-rank irreducible Killing tensors. First way is to employ the Eisenhart lift of lower-dimensional integrable systems. Second way consists of a particular lift of Killing vectors and their Casimirs. The latter procedure finds a natural application in slowly rotating black hole spacetimes where it hints on a lower-dimensional Killing vector origin of irreducible Killing tensors.

Black hole perturbations theory provides us with a powerful framework to describe the relaxation to equilibrium after a merger and derive the relaxation modes spectrum which play a key role in the black hole spectroscopy program. In this talk, I will focus on the so called algebraically special perturbations and review their role in exploring the properties of the perturbed black hole geometry. First I will discuss the case of the algebraically special linear perturbations (ASLP) of the Kerr geometry and show how one can describe this subsector of the perturbations solely using the metric formulation, using the most general twisting algebraically special solution space of vacuum General Relativity. I will first discuss a simple algorithm to solve them analytically in the small spin approximation up to third order. This provide a first concrete and rare example of perturbations of the Kerr black hole which can be treated entirely in the metric formulation. Then, I will show how this same framework allows us to study the stationary zero modes of the Kerr geometry which map the Kerr black hole to its Plebianski-Demianski vacuum extension, thus deforming the Kerr solution to the linearized Kerr-NUT and spinning C-metric. Finally, I will show that the same framework allows us to treat efficiently the effects of the backreaction of the mass and spin zero modes onto the Kerr geometry. The connection with the Newman-Penrose constants and the search for symmetries of black hole perturbations will also be discussed.

Based on: https://arxiv.org/pdf/2507.10384, https://arxiv.org/pdf/2406.08159

We will present results on the late-time asymptotics for scalar perturbations on extremal and sub-extremal black holes. We will see how these are related to conservation laws along the event horizon and null infinity. We will use these asymptotics to derive observational signatures for extremal black holes.

In this talk, I will review recent progress on the initial value formulation of effective field theories. I will then report on work in progress on the global non-linear stability of the vacuum in EFTs and late-time asymptotics of the radiation field.

Stationary black hole geometries with non-degenerate Cauchy horizons are classically unstable due to mass inflation. At extremality, mass inflation is absent, but a different dynamical instability arises: the Aretakis instability. In this work, we investigate the properties of degenerate horizons and their associated Aretakis instabilities. By studying examples with increasingly higher-order horizon degeneracy, we show that the Aretakis instability weakens as the degree of degeneracy grows. Motivated by these results, we propose a new black hole geometry characterized by an infinitely degenerate horizon, which we argue is stable under Aretakis-type perturbations and may therefore provide a concrete realization of a “graveyard” end state for these objects.

The memory effect for Robinson-Trautman waves is explicitly worked out. In a first step, we construct the combined frame rotation and coordinate transformation in which Robinson-Trautman waves are manifestly locally asymptotically flat at future null infinity. This allows us to apply well-established results on how to derive the memory effect in this context. In a second step, we construct a suitably improved generalized mass aspect that provides a local Lyapunov function for the flow in the sense that it is manifestly positive. News-free solutions are studied in detail and shown to coincide with the vacuum sector of Euclidean Liouville theory. They correspond to a boosted and rescaled Schwarzschild black hole. As a by-product, we show that the displacement and non-linear memory effects in locally asymptotically flat spacetimes at future null infinity are invariant under supertranslations and covariant under BMS4 Lorentz transformations and constant rescalings. A novel interpretation of modified flows that control the low harmonics in terms of keeping the system in its instantaneous rest frame is provided.

Asymptotically flat spacetimes are defined consistently with known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter. Under our assumptions, the relativistic gravitational field is entirely determined at leading order in the large radius expansion at spatial infinity by its supermomentum and its dual supermomentum while it is determined at subleading order by three additional sets of charges: the super-Lorentz charges, the leading tail charges and the leading peeling-breaking charges.

We prove using tools from harmonic analysis that all such charges are conserved or asymptotically conserved charges on the boundary hyperboloid at spatial infinity. Therefore, these charges obey asymptotic matching conditions between the past of future null infinity and the future of null infinity. This provides five non-trivial conservation equations of the gravitational field up to subleading order in the large radius expansion, namely at leading order: the conservation of supermomenta (which underlies the classical leading soft graviton theorem) and the conservation of the dual supermomenta, and at subleading order: the conservation of super-Lorentz charges, the leading law of breaking of peeling and the conservation of leading tails (which underlie the logarithmic subleading soft graviton theorem and the subleading soft graviton theorem).

This talk summarizes a series of three papers published in collaboration with Sébastien Robert.

The usual, "displacement" memory effect is characterized by a net change in the gravitational waveform as measured at null infinity.  Contributions to this effect split into two types: a linear, "charge" contribution given by the change in the supermomentum, and another "flux" contribution arising from nonlinearities in Einstein's equations in the propagation of gravitational waves.  For many astrophysical sources, the nonlinear flux contribution is dominant, and so its presence is often used as a criterion for the detection of memory.  In this talk, I will first discuss why this is so, and then I will generalize this picture to "higher memories", an infinite collection of similar, non-oscillatory effects.  In particular, an infinite tower of charges, first described by Newman and Penrose, each of which is exactly constant in the linear theory, plays an important role in determining which parts of these higher memories have a well-defined notion of detection in this framework.

Future null infinity is a spacetime horizon in Penrose's conformal picture, expanding or not depending on the conformal factor chosen. In both cases, it is possible to draw useful comparisons between the different symmetry groups that occur at future null infinity and at horizons. I'll review these properties, and explain why the groups are often the same or almost the same, in spite of the different dynamics and nature of the background fields present.

In this talk, I will review the application of the Newman–Penrose formalism to two null hypersurfaces of physical importance: future null infinity and a null surface at finite distance (which can be further restricted to a horizon). I will discuss the similarities and differences between these two settings, focusing mainly on the equations of motion and the Bianchi identities. Finally, I will explain how these two surfaces can be mapped through an off-shell Weyl rescaling. Based on 2511.07525.

An asymptotically flat spacetime in D = 4 can be mapped via Couch-Torrence conformal inversion into the geometry around an extremal non-expanding and non-rotating horizon. At the linearized level, an infinite tower of conserved Newman-Penrose charges can be found at null-infinity, while infinitely many Aretakis charges are conserved in the near-horizon. Couch-Torrence inversion allows one to establish a matching between the two sets of asymptotic charges. In this work we construct the Newman-Penrose and Aretakis scalar charges in higher-dimensional geometries of D3-branes in D = 10 and D3-brane bound states in D = 4 and D = 5 and establish a precise matching between them through the inversion. By exploiting the residual unbroken supersymmetry of Type IIB supergravity, we demonstrate that it is possible to relate scalar (complex dilaton) charges to higher spin charges. In particular, we determine infinite towers of conserved asymptotic spinorial charges associated with the dilatino fluctuations, and determine the map through inversion.

In this talk we will study the symmetries of asymptotically-FLRW spacetimes by focusing in detail on the three-dimensional case sourced by a scalar field. This reveals a striking analogy with four-dimensional vacuum asymptotically-flat spacetimes, and in particular the inclusion of superrotations requires to deal with issues similar to those encountered with the generalized-BMS group. After introducing a proper notion of covariant news, we show how the Cotton scalars enable to identify an analogue of the four-dimensional higher spin charges and Newman-Penrose charges.

There exist dynamical extreme Reissner-Nordstrom (DERN) black holes. These are spherically symmetric dynamical solutions of Einstein-Maxwell theory coupled to a neutral scalar that feature: (i) a spacetime metric which tends to that of a static extreme Reissner-Nordstrom (RN), and (ii) a scalar field which exhibits the linear Aretakis instability ad infinitum in the non-linear theory. We employ the two-dimensional Jackiw-Teitelboim (JT) gravity to give an explicit closed form description of the late-time near-horizon approach to DERN.

I will introduce hidden symmetries encoded in Killing and Killing-Yano tensors and discuss their role for integrability of geodesics and separability of test field equations in rotating black hole spacetimes.