General Relativity & Quantum Cosmology

I will review implications of the AdS/CFT correspondence for quantum gravity, paying particular attention to holographic RG flows and the processing of information. Deformed hyperbolic geometries correspond to boundary field theory RG flows. Conversely, as I will exemplify using the recent approach of discrete holography, boundary RG flows may be used to reconstruct the bulk spacetime, for instance via tensor networks. I will discuss recent approaches towards including gravity dynamics into this reconstruction process. --- The presenter will be joining via Zoom for this talk.

I will briefly review the key concepts underlying the Effective Field Theory of General Relativity, and give a couple of examples of how it works. Then I will describe seven lessons which can be extracted from the theory. Finally I discuss some of the limitations of the EFT framework.

 

Motivated by the static patch of de Sitter space, we discuss timelike surfaces in general relativity and the initial boundary value problem. We consider the Dirichlet problem and a conformal version thereof. Time permitting we discuss some ideas in lower dimensions.

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Zoom link https://pitp.zoom.us/j/98357788662?pwd=b3lHS3Q3T2xkNm53SkR3QVVvTGJMdz09

In general relativity, the remnant black hole of a binary black hole merger emits “ringdown” radiation: a superposition of quasinormal modes with characteristic complex frequencies. The detection of more than one of these frequencies would serve as smoking-gun evidence of a black hole and would enable a test of the no-hair theorem. In this talk, I will discuss strategies for identifying quasinormal modes within simulated ringdown waveforms both in linear perturbation theory and full general relativity. I will show that a rich spectrum of modes could exist in the ringdown, including overtones, retrograde modes and nonlinear modes, and that interesting quasi-universal relationships exist between some of their amplitudes. I will also discuss the spectral instability of quasinormal modes and its potential imprints on the ringdown waveform. These results could guide the analysis of real ringdown signals detected by gravitational-wave detectors.

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Zoom link https://pitp.zoom.us/j/92002625163?pwd=bHNDVVZKYnVNTENLNXJBLzVNKzVSQT09

Building on the fact that quantum uncertainty is a dynamical degree of freedom in itself in quantum mechanics, I will start with the remark that its evolution can provide a notion of intrinsic clock. To illustrate the non-triviality of this idea, we’ll check the dynamics of the uncertainty if gravitizing quantum mechanics into a non-linear Schrödinger equation, and will see that it (surprisingly?) follows the same trajectories as planetary orbits. A third thread will come from the black hole mini-superspace in general relativity. We will see that, assuming that the quantization preserves all the symmetries of the theory, universal quantum gravity corrections can also be written as a non-linear Schrödinger equation, leading to a non-trivial evolution of the “classicality” of black hole wave-packets along the radial coordinate.

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Zoom link: https://pitp.zoom.us/j/95808416532?pwd=cHJnVXpzdDd3eXdFbUlMamFsMFV3UT09

Anticipating the launch of several next-generation gravitational wave (GW) detectors in the 2030s, we will be able to more precisely measure spacetime ripples from binary black hole (BH) mergers in a larger parameter space. The forthcoming data will require us to develop more accurate predictions of GWs not only in General Relativity (GR) but also in theories beyond GR and diverse astrophysical environments. Black hole perturbation theory is a cornerstone for making these predictions. In recent years, there have been extensive studies of perturbations of BHs in theories beyond GR, but only for non-rotating or slowly rotating BHs. In this talk, I will present a new formalism, based on Teukolsky's seminal work in the 1970s, to study perturbations of BHs with arbitrary spin in beyond-GR theories and in more complicated astrophysical environments. I will first discuss how to derive a modified Teukolsky equation for BHs deforming perturbatively from their counterparts in GR due to beyond-GR or environmental effects and the necessary techniques to evaluate this equation. Subsequently, I will discuss some applications of this formalism. Specifically, I will prescribe utilizing this formalism to investigate the isospectrality breaking of quasinormal modes (QNMs) in beyond-GR theories, compute the QNM frequency shifts in some specific theories, and efficiently extract these shifts from observation data. Furthermore, I will also show how to apply this formalism to study extreme mass-ratio inspirals beyond GR.

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Zoom link: https://pitp.zoom.us/j/99282316326?pwd=REtBSFUxdlgxUGVwZFFvVEVBVnFTUT09

In classical relativity we usually think of the metric signature as fixed, but quantum cosmology already forces us to consider more general situations such as transitions from Riemannian to Lorentzian signature. I will discuss the less studied phenomenon of an overall "flip" where all metric components change sign simultaneously (e.g., from "East Coast" to "West Coast" signature). Such an overall flip can represent saddle point solutions in quantum cosmology, or appear classically in the Plebański formalism or even a slight extension of Einstein--Hilbert gravity. Interestingly, at such a transition the cosmological constant can change both sign and magnitude, with a pure sign change being the most minimalistic proposal. Cosmological solutions transitioning classically between de Sitter and anti de Sitter can be found immediately, and the quantisation of a minisuperspace model turns out to be simpler than in the fixed signature case: in particular, the gravitational action reduces to a pure boundary term. Various other applications and the relation to unimodular gravity are also discussed.

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Zoom link: https://pitp.zoom.us/j/93255772501?pwd=bWhzZUVBOTM2a3QvTGlXVGJ5TlZnUT09

While Einstein's theory of gravity is formulated in a smooth setting, the singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature, there is a highly successful theory of metric and metric-measure geometry which includes Riemannian manifolds as a special case, but permits the extraction of nonsmooth limits under curvature and dimension bounds analogous to the energy conditions in relativity: here sectional curvature is reformulated through triangle comparison, while Ricci curvature is reformulated using entropic convexity along geodesics of probability measures.This lecture explores recent progress in the development of an analogous theory in Lorentzian signature, whose ultimate goal is to provide a nonsmooth theory of gravity. We highlight how the null energy condition of Penrose admits a nonsmooth formulation as a variable lower bound on timelike Ricci curvature. We discuss an example showing the null energy condition does not survive the same sort of limits that uniform bounds on the timelike Ricci curvature respect. 

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Zoom link: https://pitp.zoom.us/j/92777399316?pwd=QmNaM1J0elgyRGdmaGxCTTQxT2Y4QT09

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge, which is a generalization of the FG gauge for asymptotically locally AdS (AlAdS) spacetimes. Then, the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the AlAdS bulk metric for even boundary dimensions. Under holographic renormalization, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory.

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Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. I shall describe the types of non-smooth structure that can arise on a horizon that is smooth at late time. This includes creases, corners and caustic points. I shall discuss ``perestroikas'' of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the ``instant of merger'' of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. I shall discuss the possibility that creases contribute to black hole entropy, and the implications of non-smoothness for higher derivative terms in black hole entropy. This talk is based on joint work with Maxime Gadioux.

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Zoom link: https://pitp.zoom.us/j/98839294408?pwd=cytNYThQaDV4Y2lob1REY0NyaTJNUT09

A stochastic gravitational wave background (SGWB) originates from numerous faint gravitational wave (GW) signals arising from coalescing compact binary objects. Based on the current estimated merger rate, the SGWB signal is expected to originate from non-overlapping GW waveforms where the chirping nature of individual events is expected to be preserved. In this talk, we present a novel technique, Spectrogram Correlated Stacking (or SpeCs), which goes beyond the usual cross-correlation (and to higher frequencies) by exploiting the higher-order statistics in the time-frequency domain. This method would account for the chirping nature of the individual events that comprise SGWB and enable us to extract more information from the signal due to its intrinsic non-gaussianity. We show that SpeCs improve the signal-to-noise for the detection of SGWB by a factor close to 8, compared to standard optimal cross-correlation methods which are tuned to measure only the power spectrum of the signal. SpeCs can probe beyond the power spectrum and its application to the GW data available from the current and next-generation detectors would speed up the SGWB discovery.

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Zoom link: https://pitp.zoom.us/j/91002244803?pwd=a0dnMjZEYTEwSHBCVGRSeHB2Y2pJdz09