General Relativity & Quantum Cosmology

The recent detections of gravitational waves from compact object binary
lead to detailed investigations of the origin of these objects. In my talk
I will discuss the questions: What is the astrophysical origin of these objects?
What do these detections tell us about the formation of black holes and neutron stars?
What are the main problems that they pose?
What to expect in the coming gravitational observations?

In this talk I will discuss several recent advances in loop quantum cosmology and its extension to inhomogeneous models. I will focus on spherically symmetric spacetimes and Gowdy cosmologies with local rotational symmetry in vacuum. I will discuss how to implement a quantum Hamiltonian evolution on these quantizations. Then, I will focus on how we can extract predictions from those quantum geometries, and finally analyze a concrete example: cosmological perturbations on Bianchi I spacetimes in LQC.

I suggest a minimal practical formal structure for a more fundamental theory than the Standard Model + GR and review a mechanism that produces such a structure.  The proposed mechanism has possibilities of producing non-canonical phenomena in SU(2) and SU(3) gauge theories which might allow conditional predictions that can be tested.

The slides and other writings are posted on my web page

     http://www.physics.rutgers.edu/~friedan/#Perimeter

During my visit to PI, I hope also to discuss informally a separate project in pure QFT, a scheme to construct a new kind of QFT of extended objects (also described on my web page).

The Bondi mass loss formula has been central in the context of early research on gravitational waves. We show how it can be understood as a particular case of BMS current algebra and discuss the associated central extension. We then move down to three dimensions where a more complete picture emerges.

Canonical quantization schemes often suggest modifications to classical dynamics, such as in an effective Friedmann equation. However, although often ignored, they also necessarily imply new effects for quantum space-time leading to new (quantum) symmetries. The invariant line-element, corresponding to  new geometrical structures emerging in the presence of holonomy modifications in loop quantum gravity, shall be consistently derived in this talk. We shall use black-hole models to illustrate new features of this quantum space-time, going beyond standard Riemannian manifolds.

In the first part of the talk, I will describe the new large N limit of tensor models, based on the “index” of graphs (in contrast to the standard large N expansion  based on the “degree”), and the associated new large D limit of matrix models. This new limit sheds an interesting light on the relation between disordered models à la SYK, tensor models and black holes. In the second part of the talk, I will apply these ideas to discuss the phase diagrams of some strongly coupled matrix quantum mechanics. The phase diagrams display many interesting features, including first and second order phase transitions and quantum critical points. Some of these phase transitions can be argued to provide a quantum mechanical description of the phenomenon of gravitational collapse. 

Detections of compact binary coalescences with Advanced LIGO and Advanced Virgo are now starting to become routine. However, thereis still considerably more information that can be gleaned from these observations, particularly as detector sensitivity and waveform modelsboth improve. We start by describing the methods currently used in LIGO/Virgo data analysis to determine the mass and spin of the remnant black hole of the binary black hole coalescences. These black holes have the most well-measured masses and spins of any stellar-mass black holes observed and comparable or better mass accuracies to Sgr A*. We also describe the method used to obtain a lower bound on the radiated energy of the binary neutron star coalescence GW170817, and discuss further information one can extract from these observations by postprocessing parameter estimation results. We also describe a method for placing constraints on properties of black hole mimickers, such as boson stars or gravastars, if binaries of these objects are to produce the signals identified as coming from binary black holes. We present initial results of the method applied to injections in simulated noise, and as a proof of principle show how it is possible to rule out or constrain the properties of a specific model of boson stars using a given detection.

In this talk, I will summarize the status of the numerical evaluation of spin foam amplitudes focusing on the Lorentzian EPRL-FK model. I will illustrate how numerical methods can lift some limitations of the theory helping us understand better its continuum and semi-classical limit.

The causal structure of spacetimes containing fully evaporated black holes is considered from the perspective of Lorentzian geometry. The starting point is provided by theorems, due to Kodama, Geroch and Wald, that derive non-global hyperbolicity from a set of premises relating two partial Cauchy surfaces that are thought of as, respectively, lying before and after the evaporation. Here, we consider the Geroch-Wald theorem in the setting of a conformally embedded spacetime a la Penrose and show, under the assumption that complete null geodesics outside the black hole reach the boundary, that there exists visible incomplete null geodesics and that causal continuity fails.

The talk will focus on issues connected with the quantization of initial data for vacuum general relativity on null hypersurfaces. Complete and constraint free initial data for GR can be given on pairs of intersecting null hypersurfaces. These offer a route to a canonical quantization of GR which avoids having to deal with constraints. However the Poisson algebra of these data is rather intricate and it is not obvious how one might quantize it. This algebra is however almost the same in the cylindrically symmetric case as in the full theory, which suggests that the cylindrically symmetric theory ought to offer valuable insights. Here I present recent joint work with Javier Peraza and Miguel Paternain relating the Poisson algebra in the cylindrically symmetric case to well studied algebraic structures.