School of Mathematical Sciences

SCEENAC 2019 Schedule

SCEENAC 2019 Schedule

Conference Talks

Time Thursday Sept 12 Friday Sept 13
09:00-09:30 Welcome/Registration
09:30-10:30 Adam Pound (University of Southampton) Chris Fewster (University of York)
10:30-11:00 Coffee Break Coffee Break
11:00-12:00 Igor Khavkine (Czech Academy of Sciences) Noa Zilberman (Technion)
12:00-14:00 Lunch Lunch
14:00-15:00 Hanno Gottschalk (Bergische Universität Wuppertal) Helvi Witek (King's College London)
15:00-15:30 Coffee Break Coffee Break
15:30-16:30 Marc Casals (CBPF) Markus Fröb (Universität Leipzig)
16:30-17:30 Nicola Pinamonti (University of Genova)
18:30-19:30 Public Lecture by Chris Fewster

Public Lecture

The public lecture will be held on the evening of Thursday, Sept 12th, 6:30pm-7:30pm. This will take place on the DCU St. Patrick's Campus, the room TBC.

This is a ticketed event, but there is no charge for attendance, and all are welcome. For further details and/or to register, please click here.

Abstracts for Workshop

  • Author: Adam Pound
  • Title: Regularization methods in gravitational self-force theory.
  • Abstract: I discuss various (equivalent) regularisation methods in gravitational self-force theory. I emphasise their derivation from matched asymptotic expansions and their interpretation as a method of solving a free boundary value problem involving no singular quantities, before describing various practical issues that arise in their implementation.

  • Author: Igor Khavkine
  • Title: Renormalization of Wick polynomials of locally covariant bosonic vector valued fields
  • Abstract: In perturbative algebraic QFT on curved spacetime, the axioms of local covariance impose strong conditions on possible renormalization schemes for local composite operators, like Wick polynomials. Building on previous work for scalar fields, we fully classify the ambiguity (aka finite renormalization freedom) in the consistent definition of renormalized Wick polynomials of general bosonic vector valued fields. Our results rely on tools from the theory of differential invariants of (pseudo-)Riemannian spaces, and classical invariants of general linear and orthogonal groups. This is based on the joint works [arXiv:1411.1302,1710.01937] with Valter Moretti and/or Alberto Melati.

  • Author: Hanno Gottschalk
  • Title: The Cosmological Semiclassical Einstein Equation as an Infinite Dimensional System: Existence and Stability of Solutions for all Couplings.
  • Abstract: We give a formulation of the semiclassical Einstein equation in cosmological space times as an infinite dimensional dynamical system for general coupling. One of the problems in doing so is the observation that in general this equation is of fourth order in the scale factor and the same order of derivatives occurs in the renormalization terms of the energy-momentum tensor. Therefore there is no easy way in rewriting this set of equations as a dynamical system, as the highest order derivative of the scale factor can not be isolated on the left hand side of the trace equation. However, recasting the system into an infinite tower of 'renormalized momenta' of the state allows us to formulate a dynamical system for such renormalized momenta that naturally couples to the trace equation. We prove existence, uniqueness and maximality of solutions for this dynamical systems for the 'renormalized momenta' located in certain spaces. We also show that these spaces are sufficiently large to contain the most relevant physical states - vacuum and thermal like states in particular. The talk is based on joint work with Daniel Siemssen.

  • Author: Marc Casals
  • Title: Analytic solutions of the semiclassical equations for rotating black hole and naked singularity backgrounds in 2+1-dimensions.
  • Abstract: We analytically solve the semiclassical Einstein equations where the source is the quantum stress-energy tensor for a scalar field on a given classical background. This classical background is the (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) space-time, in both cases that it represents a rotating black hole and a rotating naked singularity. The solution that we obtain is the quantum-backreacted space-time and we study its properties with respect to the background space-time: in the black hole case, the Cauchy horizon has become unstable in some region of parameter space (e.g., near maximal rotation); in the naked singularity case, an event horizon has formed around the singularity. These results support the role of quantum physics as a Cosmic Censor in Nature. (This talk is based on Phys. Rev. Lett. 118, 131102, 2017, and Phys. Rev. D 99, 104023, 2019)

  • Author: Nicola Pinamonti
  • Title: Solutions of the semiclassical Einstein equations in cosmological spacetimes and their fluctuations.
  • abstract:
  • Abstract: During this talk we shall discuss the influence of quantum matter on classical curvature. More precisely, we shall describe matter as a quantum field propagating on a curved background. Furthermore, since matter will be of quantum nature, the Einstein equations governing its backreaction on curvature will assume a probabilistic interpretation. We will thus see how the singular structure of quantum matter states will affect the spectrum of metric fluctuations on a cosmological background.

  • Author: Chris Fewster
  • Title: Singularity theorems with weakened energy hypotheses inspired by QFT
  • Abstract: The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri's equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by Quantum Energy Inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply. The talk will be largely based on arXiv:1907.13604 (joint work with E.-A. Kontou) and will introduce index form methods from the start.

  • Author: Noa Zilberman
  • Title: Semiclassical energy-momentum fluxes at the inner horizon of a spherical charged black hole.
  • Abstract: The analytically extended Kerr and Reissner-Nordström (RN) geometries reveal a smoothly-traversable passage through an inner horizon (IH) to another external universe. But does such an "inter-universal" tunnel really exist inside realistic astrophysical black holes (BHs)? It is widely anticipated that semiclassical effects would diverge at the IH. Such a divergence, if indeed takes place, may have a drastic effect on the internal BH geometry, potentially preventing the IH traversability. But do semiclassical effects really diverge at the IH? And if they do, then in what rate? Are they capable of significantly affecting (or even preventing) the IH traversability? These questions (among others) were left inconclusive until now. The basic physical quantity needed for exploring this question is the renormalized stress-energy tensor, and more specifically the flux components <Tvv > and <Tuu > (u and v being the Eddington coordinates), at the IH limit. However, the computation of these quantities has been a serious challenge for decades, leaving the issue inconclusive. However, the recently developed pragmatic mode-sum regularization method has made the computation more accessible. In this talk, following a review of the regularization procedure, we shall present novel results for the energy-momentum fluxes, for a minimally-coupled massless scalar field, at the IH of a RN BH. As we shall see, these quantum fluxes indeed have a divergent effect at the IH. We will characterize the strength of this divergence, as well as its magnitude and sign, as a function of Q/M. Special attention will be given to the near-extremal limit, which lends itself to analytical treatment. We will end with a preliminary discussion on possible implications for the backreaction.

  • Author: Helvi Witek
  • Title: Numerical relativity in modified gravity
  • Abstract: Both observations and deeply theoretical considerations indicate that general relativity, our elegant standard model of gravity, requires modifications at high curvatures scales. Candidate theories of quantum gravity, in their low-energy limit, typically predict couplings to additional fields or extensions that involve higher curvature terms. At the same time, the breakthrough discovery of gravitational waves has provided a new channel to probe gravity in its most extreme, strong-field regime. Modelling the expected gravitational radiation in these extensions of GR enables us to search for -- or place novel observational bounds on -- deviations from our standard model. In this talk I will give an overview of the recent progress on simulating binary collisions in these situations as well as renewed mathematical challenges such as well-posedness of the underlying initial value formulation.

  • Author: Markus Fröb
  • Title: Beyond the SEE: quantum gravitational backreaction in inflation.
  • Abstract: In addition to quantised matter fields that enter the semiclassical Einstein equation, we consider also quantised metric perturbations. While at tree level they give the observed power spectrum of the CMB, loop corrections backreact on the semiclassical geometry. An important open question is how to quantify this backreaction physically. We present a recent proposal and results at one-loop order. (Based on arXiv:1806.11124 and arXiv:1711.08470.)