Past Relativity Seminar

In recent years, the theme of asymptotically flat spacetimes has come back to the fore, fueled by the discovery of gravitational waves and the growing interest in what flat holography could be. In this quest, the standard tools pertaining to asymptotically anti-de Sitter spacetimes have been insufficiently exploited. I will show how Ricci-flat spacetimes are generally reached as a limit of Einstein geometries and how they are in fact constructed by means of data defined on the conformal Carrollian boundary that is null infinity. These data, infinite in number, are obtained as the coefficients of the Laurent expansion of the energy-momentum tensor in powers of the cosmological constant. This approach puts this tensor back at the heart of the analysis, and at the same time reveals the versatile role of the boundary Cotton tensor. Both appear in the infinite hierarchy of flux-balance equations governing the gravitational dynamics.  

This will be an informal discussion seminar based on https://arxiv.org/abs/2211.07592:

The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS4 generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS4 Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.

We present a new formulation of string and particle amplitudes that emerges from simple one-dimensional models. The key is a new way to parametrize the positive part of Teichmüller space. It also builds on the results of Mirzakhani for computing Weil-Petterson volumes. The formulation works at all orders in the perturbation series, including non-planar contributions. The relationship between strings and particles is made manifest as a "tropical limit". The results are well adapted to studying the scattering of large numbers of particles or amplitudes at high loop order. The talk will in part cover results from arXiv:2309.15913, 2311.09284.

Recently, the Newman-Janis shift has been revisited from the angle of scattering amplitudes in terms of the so-called "massive spinor-helicity variables," tracing back to Penrose and Perjés in the 70s. However, well-established results are limited in the same-helicity (self-dual) sector, while a puzzle of spurious poles arises in mixed-helicity sectors. This talk will outline how massive twistor theory can reproduce the same-helicity results while offering a possible solution to the spurious pole puzzle. Firstly, the Newman-Janis shift in the same-helicity sector is derived from a complexified version of the equivalence principle. Secondly, the massive twistor particle is coupled to background fields from bottom-up and top-down perspectives. The former is based on perturbations of symplectic structures in massive twistor space. The latter provides a generalization of Newman-Janis shift in generic backgrounds, which also leads to "curved massive twistor space" and its deformed massive incidence relation. Lastly, the Feynman rules of the first-quantized massive twistor particle and their physical interpretation are briefly discussed. Overall, a significant emphasis is put on the Kähler geometry ("zig-z̄ag structure") of massive twistor space, which eventually connects to a worldsheet structure of the Kerr solution.

I will show that the massless irreducible representations of the Poincare group are precisely Corrolian field living on I^+. I will also show that the analogous massless irreducible representation of E11 are just the degrees of freedom of maximal supergravity. Finally I will speculate how spacetime could emerge from an underlying fundamental theory.

The Celestial Holography program encompasses recent efforts to understand the flat space hologram in terms of a CFT living on the celestial sphere. Here we have fun relating various extrapolate dictionaries in CCFT and examining tools we can apply when perturbing around a 4D CFT in the bulk.

Hydrodynamics allow for efficient computation of many-body dynamics and have been successfully used in the study of black hole horizons, collective behaviour of QCD matter in heavy ion collisions, and non-equilibrium behaviour in strongly-interacting condensed matter systems.
In this talk, I will present the application of hydrodynamics to quantum field theory with an infinite number of local conservation laws. Such an integrable system can be described within the recently developed framework of generalised hydrodynamics. I will present the key assumptions of generalised hydrodynamics as well as summarise some recent developments in this field. In particular, I will concentrate on the study of the SU(3)_2-Homogeneous sine-Gordon model. Thanks to the hydrodynamic approach, we were able to identify the key dynamical signatures of unstable excitations in this integrable quantum field theory and simulate the real time RG-flow of the theory between interacting and free conformal regimes.
The talk is based on joint work with Olalla Castro-Alvaredo, Cecilia De Fazio and Benjamin Doyon.

In this talk I will review some of the key ideas behind the study of entanglement measures in 1+1D quantum field theories employing the so-called branch point twist field approach. This method is based on the existence of a one-to-one correspondence between different entanglement measures and different multi-point functions of a particular type of symmetry field. It is then possible to employ standard methods for the evaluation of correlation functions to understand properties of entanglement in bipartite systems. Time permitting, I will then present a recent application of this approach to the study of a new entanglement measure: the symmetry resolved entanglement entropy.

Black hole horizons are normally at finite spatial distance from the exterior region, but when they are degenerate (or extreme as they are usually referred to in this case) the spatial distance becomes infinite. One can still fall into the black hole in finite proper time but the crossing sphere is replaced by an "internal infinity". Near to the horizon of an extreme Kerr black hole, the scattering properties of test fields bear some similarities to what happens at an asymptotically flat infinity. This observation triggered a natural question concerning the peeling behaviour of test fields near such horizons. A geometrical tool known as the Couch-Torrence inversion is particularly well suited to studying this question. In this talk, I shall recall some essential notions on the peeling of fields at an asymptotically flat infinity and describe the Couch-Torrence inversion in the particular case of extreme Reissner-Nordström black holes, where it acts as a global conformal isometry of the spacetime. I will then show how to extend this inversion to more general spherically symmetric extreme horizons and describe what results can be obtained in terms of peeling. This is a joint ongoing project with Jack Borthwick (University of Besançon) and Eric Gourgoulhon (Paris Observatory).

Holography in asymptotically flat spaces is one of the most coveted goals of modern mathematical physics. In this talk, I will motivate a novel holographic description of self-dual SO(8) Yang-Mills + self-dual conformal gravity on a Euclidean signature, asymptotically flat background called Burns space. The holographic dual lives on a stack of D1-branes wrapping a CP^1 cycle in the twistor space of R^4 and is given by a gauged beta-gamma system with SO(8) flavor and a pair of defects at the north and south poles. It provides the first example of a stringy realization of (asymptotically) flat holography and is a Euclidean signature variant of celestial holography. This is based on ongoing work with Kevin Costello and Natalie Paquette.

A particle physics approach to describing black hole interactions is opening new avenues for understanding gravitational-wave observations. We will start by reviewing this paradigm change, showing how to compute observables in general relativity from amplitudes on flat spacetime. We will then present a generalization of this framework for amplitudes on curved backgrounds. Evaluating the required one-to-one amplitudes already shows remarkable structures. We will discuss them in detail, including eikonal behaviours and unexpected KLT-like factorization properties for amplitudes on stationary backgrounds. We will then conclude by discussing applications of these amplitudes to strong field observables such as the impulse on a curved background and memory effects

Non-shearing congruences of null geodesics on four-dimensional Lorentzian manifolds are fundamental objects of mathematical relativity. Their prominence in exact solutions to the Einstein field equations is supported by major results such as the Robinson, Goldberg-Sachs and Kerr theorems. Conceptually, they lie at the crossroad between Lorentzian conformal geometry and Cauchy-Riemann geometry, and are one of the original ingredients of twistor theory.
 
Identified as involutive totally null complex distributions of maximal rank, such congruences generalise to any even dimensions, under the name of Robinson structures. Nurowski and Trautman aptly described them as Lorentzian analogues of Hermitian structures. In this talk, I will give a survey of old and new results in the field.

In the first part of this talk, we will (briefly) derive the original calculation by Hawking in 1974 to determine the radiation given off by a black hole, giving the result in the form of an integral of a classical solution to the linear wave equation.
In the second part of the talk, we will take this integral as a starting point, and rigorously calculate the radiation given off by a forming spherically symmetric, charged black hole. We will then show that for late times in its formation, the radiation given off approaches the limit predicted by Hawking, including the extremal case. We will also calculate a bound on the rate at which this limit is approached.

I'll argue that the celestial holography program looks a lot like the twisted holography program when studied on twistor space.  The chiral algebras in celestial holography can be seen by applying techniques such as Koszul duality to holomorphic theories on twistor space. Along the way, I will discuss the role of one-loop gauge anomalies on twistor space and when they can be cancelled by a Green-Schwarz mechanism.   This is joint work in progress with Natalie Paquette.

The speaker will be on zoom, but for a more interactive experience, some of the audience will watch the seminar in L5.

The recent progress of applying QFT methods to classical GR has provided a new perspective on the Kerr black hole solution. Its leading gravitational interactions are known to involve an infinite tower of spin-induced multipoles with unit coupling constants. In this talk, I will present a novel form of the classical worldline action that implements these multipole interactions within a single worldsheet integral, which is inspired by the Newman-Janis shift relationship of the Kerr and Schwarzschild solutions. I will also discuss connections to our recently discovered ability to model such interactions using a certain family of scattering amplitudes, as well as a simple double-copy property hidden within. 

This will be an in-person seminar run in hybrid mode.

Penrose's proposal of smooth conformal compactification is not only of geometric elegance, it also makes concrete predictions on physically measurable objects such as the "late-time tails" of gravitational waves.  At the same time, the physical motivation for a smooth null infinity remains itself unclear. In this talk, building on arguments due to Christodoulou, Damour and others, I will show that, in generic gravitational collapse, the "peeling property" of gravitational radiation is violated (so one cannot attach a smooth null infinity). Moreover, I will explain how this violation of peeling is in principle measurable in the form of leading-order deviations from the usual late-time tails of gravitational radiation.

This talk is based on https://arxiv.org/abs/2105.08079, https://arxiv.org/abs/2105.08084 and … .

It will be a hybrid seminar on both zoom and in-person in L5. 

We will present the precise late-time asymptotics for scalar fields on both extremal and sub-extremal black holes including the full Reissner-Nordstrom family and the subextremal Kerr family. Asymptotics for higher angular modes will be presented for all cases. Applications in observational signatures will also be discussed. This work is joint with Y. Angelopoulos (Caltech) and D. Gajic (Cambridge)

I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

Plebanski generating functions give a compact encoding of the geometry of self-dual Ricci-flat space-times or hyper-Kahler spaces.  They have applications as generating functions for BPS/DT/Gromov-Witten invariants.  We first show that Plebanski's first fundamental form also provides a generating function for the gravitational MHV amplitude.  We then obtain these Plebanski generating functions from the corresponding twistor spaces as the value of the action of new sigma models for holomorphic curves in twistor space.   
In four-dimensions, perturbations of the hyperk¨ahler structure corresponding to positive helicity gravitons. The sigma model’s perturbation theory gives rise to a sum of tree diagrams for the gravity MHV amplitude observed previously in the literature, and their summation via a matrix tree theorem gives a first-principles derivation of Hodges’ determinant formula directly from general relativity. We generalise the twistor sigma model to higher-degree (defined in the first instance with a cosmological constant), giving a new generating principle for the full tree-level graviton S-matrix in general with or without  cosmological constant.  This is joint work with Tim Adamo and Atul Sharma in https://arxiv.org/abs/2103.16984.  

The outstanding issue of a non-singular extension of the Kerr-NUT- (anti) de Sitter solutions to Einstein’s equations is solved completely. The Misner’s method of obtaining the extension for Taub-NUT spacetime is generalized in a non-singular manner. The Killing vectors that define non-singular spaces of non-null orbits are derived and applied. The global structure of spacetime is discussed. The non-singular conformal geometry of theinfinities is derived. The Killing horizons are present.

The propagation of high-frequency electromagnetic waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of light in an inhomogenous medium via a spin-orbit coupling mechanism. This effect, known as the spin Hall effect of light, has been experimentally observed. In this talk I will discuss recent work which generalizes the spin Hall effect to the propagation of light and gravitational waves in inhomogenous spacetimes. This is based on joint work with Marius Oancea and Jeremie Joudioux.