General Relativity & Quantum Cosmology

The goal of this talk is to discuss residual gauge symmetries in electromagnetism and gravity in Dirac's front form. Working in the light-cone gauge, I will demonstrate how the large gauge transformations and BMS supertranslations may be obtained from residual gauge invariance of the Hamiltonian action. The residual gauge symmetries in this (2+2) formulation share some striking similarities with the asymptotic symmetries in the conventional (3+1) Hamiltonian formulation. I will illustrate this fact using the example of electromagnetism and show how the the zero modes play a crucial role akin to boundary degrees of freedom in the asymptotic analysis at spatial infinity à la Henneaux-Troessaert.

In this introductory talk, I will present a new perspective about quantum gravity which is rooted deeply in a renewed understanding of local symmetries in Gravity that appears when we decompose gravitational systems into subsystems. I will emphasize the central role of the corner symmetry group in capturing all the necessary data needed to glue back seamlessly quantum spacetime regions. I will present how the charge conservation associated with these symmetries encoded the dynamics of null surfaces. Finally, I will also present how the representation theory of the corner symmetry arises and provides a representation of quantum geometry, and I will show that deformations of this symmetry can be the explanation for a fundamental planckian cut-off. I will also mention how these symmetry groups reduce to asymptotic symmetry groups and control asymptotic gravitational dynamics when the entangling sphere is moved to infinity. If time permits, I will explain how these symmetries control asymptotic gravitational dynamics. And I will describe how they provide a new picture of the nature of quantum radiation. Overall, this new paradigm allows to connect semi-classical gravitational physics, S-matrix theory, and non-perturbative quantum gravity techniques. The talk's goal is to give an overall flavor of how these connections appear from an elementary understanding of symmetries.

Speaker Order: Ankit Aggarwal, University of Amsterdam Monireh Ahmadpour, University of Tehran Giovanni Canepa, Centre de Physique Théorique Roukaya Dekhil, Ludwig Maximilian University Arnaud Delfante, University of Mons Florian Ecker, Technische Universität Wien Gloria Odak, Centre de Physique Théorique

We begin by reviewing the role of coadjoint orbits in the representation theory of nilpotents groups and then, to connect with the recent applications in physics of coadjoint orbits "around the corner" of the mathematical framework developed by Kirillov, we review the classification of coadjoint orbits of the Virasoro group. This will allow us to connect with more recent developments, including e.g. the study of coadjoint orbits of BMS algebras.

This lecture aims at introducing the notion of asymptotic symmetries in gravity and the derivation of the related surface charges by means of covariant phase space techniques. First, after a short historical introduction, I will rigorously define what is meant by “asymptotic symmetry” within the so-called gauge-fixing approach. The problem of fixing consistent boundary conditions and the formulation of the variational principle will be briefly discussed. In the second part of the lecture, I will introduce the covariant phase space formalism, as conceived by Wald and coworkers thirty years ago, which adapts the Hamiltonian formulation of classical mechanics to Lagrangian covariant field theories. With the help of this fantastic tool, I will elaborate on the construction of canonical surface charges associated with asymptotic symmetries and address the crucial questions of their conservation and integrability on the phase space. In the third and last part, I will conclude with an analysis of the algebraic properties of the surface charges, describing in which sense they represent the asymptotic symmetry algebra in full generality, without assuming conservation or integrability. For pedagogical purposes, the theoretical concepts will be illustrated throughout in the crucial and well-known case of radiative asymptotically flat spacetimes in four dimensions, as described by Einstein’s theory of General Relativity, and where many spectacular and unexpected features appear even in the simplest case of historical asymptotically Minkowskian boundary conditions. In particular, I will show that the surface charge algebra contains the physical information on the flux of energy and angular momentum at null infinity in the presence of gravitational radiation.

With over a hundred detections to date, the discoveries of compact binary mergers by gravitational wave observatories LIGO and Virgo have allowed us to start characterizing the astrophysical population of binary black holes. This task requires measuring the fifteen parameters (masses, spins, location, orientation, etc...) that characterize each merger event. However, these high dimensional distributions are challenging to describe due to the presence of nonlinear correlations and multiple modes. In this seminar I will describe a series of coordinate changes that, by identifying parameter combinations that control specific observable signatures in the data, remove these degeneracies and multimodality, making parameter estimation amenable. Among the new coordinates is a spin azimuth that can be measured surprisingly well in several cases, hinting that some black hole spins are misaligned with the orbit. This is very interesting because the degree of spin-orbit alignment is a robust discriminator between isolated and dynamical formation channels, which predict spins preferentially aligned with the orbit or randomly oriented, respectively. At the same time, I will show that the observed proportion of events with spins aligned versus anti-aligned with the orbit disfavors the hypothesis that the spin distribution is isotropic.

Zoom link:  https://pitp.zoom.us/j/91820222881?pwd=YW9vR0xwTlBCVXg4UlRBNWxuUFhCQT09

In this talk  will develop Rafael D. Sorkin's heuristic that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity can provide an objective physical correlate of our perception of time passing. I will argue that one cannot have an external, fully objective picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal ``view'' of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what ``breathes fire'' into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.

Zoom link: https://pitp.zoom.us/j/95170823205?pwd=QW9YM3QrZU12Ti9HTUQ4TDlVNmN5Zz09

In this talk, I present a novel framework to do black-hole spectroscopy. This approach is based on a new technique so-called “quasinormal-mode filter”, which can be classified into two subsets: rational filter and full filter. On the theoretical level, I explain how to use the rational filter to understand the ringdown of numerical-relativity waveforms. On the observational level, I introduce a way to incorporate the filter into Bayesian analysis. The new Bayesian framework not only allows us to analyze the ringdown of a real gravitational-wave event without Markov chain Monte Carlo, but also yields a natural estimate of the ringdown start time. By applying our method to GW150914, we find strong and self-consistent evidence for the first overtone from multiple perspectives. On the other hand, the relationship between the full filter and the metric reconstruction is discussed. Its connection to a numerical-relativity technique “Cauchy-characteristic Matching” is provided. In the final part of the talk, I also briefly present our recent progress on fully relativistic 3D Cauchy-characteristic Matching.

Zoom link: https://pitp.zoom.us/j/95593408817?pwd=U2RXZDV2WUtwNDlaRDVBVTJjTEdBQT09

Though often not spelled out explicitly, dynamical reference frames appear ubiquitously in gauge theory and gravity. They appear, for example, when constructing dressed/relational observables, describing physics relative to the frame in a gauge-invariant way. In this talk, I will sketch a general framework for constructing such frames and associated relational observables. It unifies previous approaches and encompasses the transformations relating different frame choices. In gravitational theories, this gives rise to an arguably more physical reformulation of general covariance in terms of dynamical rather than fixed frames. I will then discuss an ensuing relational form of locality, including bulk microcausality and local subsystems associated with subregions, both of which can be defined gauge-invariantly relative to a dynamical frame. In the latter case, the frame incarnates as an edge mode field, linking with recent work on finite subregions. In particular, the corresponding boundary charges and symmetries can be understood in terms of reorientations of the frame. Notably, the resulting notion of a subsystem is frame-dependent, as are therefore correlations, thermal properties and specifically entropies. I will conclude with an outlook on the quantum realm and connections with recent developments on quantum reference frames. [Based on 2206.01193, 2205.00913, JHEP 172 (2022), PRL 128 170401.] 

Zoom link: https://pitp.zoom.us/j/97735460640?pwd=NThybFc3M3Z3cHhVRmRvczdrclhvZz09

There exists a solid framework to study gravitational waves in full, non-linear general relativity when the spacetime is asymptotically flat. An essential aspect of this framework is asymptotic symmetries. These symmetries are the BMS symmetries. The situation for cosmological spacetimes is different, however. Expanding spacetimes, whose expansion is decelerating such as matter- or radiation-dominated universes, share some similarities with the asymptotically flat case nonetheless. Not surprisingly, their asymptotic symmetries also share similarities with the BMS symmetries, but are not the same.

Zoom Link:  https://pitp.zoom.us/j/98168915236?pwd=ejFtaVpVZXAxT2NIdDhtMUNSbmRvQT09