General Relativity & Quantum Cosmology

As was realized by Bondi, Metzner, van der Burg, and Sachs (BMS), the symmetry group of asymptotic infinity is not the Poincaré group, but an infinite-dimensional group called the BMS group. Because of this, understanding the BMS frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms and comparisons with other waveform models are performed properly. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this talk, I will highlight new methods that have led to improved numerical waveforms; specifically, I will explain what the gravitational memory effect is and how it has recently been resolved in numerical relativity. Following this, I will then illustrate how we fix the BMS frame of numerical waveforms to perform much more accurate comparisons with either quasi-normal mode or post-Newtonian models. Last, I will briefly highlight  some exciting results that this work has enabled, such as building memory-containing surrogate models and finding nonlinearities in black hole ringdowns.

Zoom Link:  https://pitp.zoom.us/j/96739417230?pwd=Tm00eHhxNzRaOEQvaGNzTE85Z1ZJdz09

I will describe a holographic model for the three dimensional de Sitter static patch where the boundary theory is the so called $T\bar{T}+\Lambda_2$ deformation of the conformal field theory dual to AdS_3 quantum gravity. This identification allows us to obtain the cosmic horizon entropy from a microstate count, and the microstates themselves are a dressed version of those that account for the entropy of certain black holes in AdS space. I will also show how the effect of this dressing at the cosmic horizon is to replace the spacetime dependence of the fields of the undeformed holographic CFT with dependence on the indices of large matrices.

Zoom link:  https://pitp.zoom.us/j/95396921570?pwd=NGFoOGlGY1ZDU2pnNFRwWit3b2w0Zz09

A gravitational wave from a binary black hole merger is an important probe to test gravity. Especially, the observation of ringdown may allow us to perform a robust test of gravity as it is a superposition of excited quasi-normal (QN) modes of a Kerr black hole. The excitation factor is an important quantity that quantifies the excitability of QN modes and is independent of the initial data of the black hole.

In this talk, I will show which QN modes can be important (i.e., have higher excitation factors) and will discuss how we can determine the start time of ringdown to maximally enhance the detectability of the QN modes. 

Also, I will introduce my recent conjecture on the modeling of ringdown waveform:

the thermal ringdown model in which the ringdown of a small mass ratio merger involving a spinning black hole can be modeled by the Fermi-Dirac distribution.

Zoom link:  https://pitp.zoom.us/j/96739417230?pwd=Tm00eHhxNzRaOEQvaGNzTE85Z1ZJdz09

I discuss novel symmetries of perturbation theory around rotating and non-rotating black holes in general relativity, and discuss their origins and implications for gravitational-wave astronomy. This is motivated by two special aspects of black hole perturbations in four dimensions: isospectrality of quasinormal modes and the vanishing of tidal Love numbers. There turn out to be off-shell symmetries underlying each of these phenomena. One is a duality, which on shell reproduces the famous Chandrasekhar duality and therefore underlies isospectrality, and can be thought of as an extension of electric-magnetic duality to black hole backgrounds. The other is a set of "ladder symmetries" relating modes of different angular momentum or spin, which imply the vanishing of Love numbers. This has a geometric origin in the conformal symmetry of low-frequency modes.

Zoom link:  https://pitp.zoom.us/j/93633894223?pwd=cEFRYno5WSt5NUJlOWJLdVZHWjE1QT09

One fruitful strategy of tackling quantum gravity is to adapt quantum field theory to the situation where spacetime geometry is dynamical, and to implement diffeomorphism symmetry in a way that is compatible with regularization and renormalization. It has taken a while to address the underlying technical and conceptual challenges and to chart a quantum field-theoretic path toward a theory of quantum gravity that is unitary, essentially unique and can produce "numbers" beyond perturbation theory. In this context, the formulation of Causal Dynamical Triangulations (CDT) is a quantum-gravitational analogue of what lattice QCD is to nonabelian gauge theory. Its nonperturbative toolbox builds on the mathematical principles of “random geometry” and allows us to shift emphasis from formal considerations to extracting quantitative results on the spectra of invariant quantum observables at or near the Planck scale. A breakthrough result of CDT quantum gravity in four dimensions is the emergence, from first principles, of a nonperturbative vacuum state with properties of a de Sitter universe. I will summarize these findings, highlight the nonlocal character of observables in quantum gravity and describe the interesting physics questions that are being tackled using the new notion of quantum Ricci curvature.

Zoom Link: https://pitp.zoom.us/j/92791576774?pwd=VEg3MEdKOWsxOEhXOHVIQUhPcUt0UT09

The growing catalog of gravitational-wave signals from compact object mergers has allowed us to study the properties of black holes and neutron stars more precisely than ever before and has opened a new window through which to probe the earliest moments in our universe’s history. In this talk, I will demonstrate how current and future gravitational-wave observations can be uniquely leveraged to learn about astrophysics and cosmology. With the current catalog of events detected by the LIGO and Virgo gravitational-wave detectors, I will present evidence for a correlation between the redshift and spin distributions of binary black holes and discuss its astrophysical implications. With joint observations of short gamma-ray bursts and binary neutron star mergers accessible in the next few years, I will describe how to constrain the jet geometry and shed light on the central engine powering these explosions. Finally, with the sensitivities expected for the next generation of gravitational-wave detectors, I will present the statistically optimal method for the simultaneous detection of a foreground of compact binary mergers and a stochastic gravitational-wave background from early-universe processes.

Zoom Link: https://pitp.zoom.us/j/95280675686?pwd=RThMeStWeWl1VlBuV1cvYW8zTXgydz09

Abstract and

Zoom Link: https://pitp.zoom.us/j/91762985902?pwd=djhwYVdsQ25GVVBRVTlwSkQvaDJ4Zz09

In this talk, I will show that supergravity on asymptotically flat spaces possesses a (nonlinear) asymptotic symmetry algebra, containing an infinite number of fermionic generators. Starting from the Hamiltonian action for supergravity with suitable boundary conditions on the graviton and gravitino fields, I will derive a graded extension of the BMS_4 algebra at spatial infinity, denoted by SBMS_4. These boundary conditions are not only invariant under the SBMS_4 algebra, but lead to a fully consistent canonical description of the supersymmetries, which have well-defined Hamiltonian generators. One finds, in particular, that the graded brackets between the fermionic generators yield BMS supertranslations, of which they provide therefore “square roots”.  I will comment on some key aspects of extending the asymptotic analysis at spatial infinity to fermions and on the structure of the SBMS_4 algebra in terms of Lorentz representations.

Zoom link: https://pitp.zoom.us/j/95951230095?pwd=eHIwUXB5SUkvd0IvZnVUN3JJMFE1QT09