Abstract: In classical General Relativity, determinism means that the values of fields on spacetime are obtainable uniquely from their values at an initial time. However, it may occur that the spacetime under consideration is part of a larger spacetime where the evolution, therefore, is not entirely determined by the initial data. This occurs, for example, in the well-known (maximally extended) Reissner-Nordström or Reissner-Nordström-deSitter spacetimes. The “edge” of the region determined by the initial data is called the “Cauchy horizon”. It is located inside the black hole. In order to address the problem of indeterminacy beyond this horizon, it has been proposed a long time ago that the Cauchy horizon is, in fact, not existent in practice because the slightest perturbation (e.g. of the metric itself or the matter fields) will catastrophically blow up on there, thereby converting it into a singularity. Recently, however, it has been observed that, classically this is not the case provided the mass, charge, and cosmological constant are in a certain regime. In this paper, we provide arguments that, in such a case, quantum theory comes to the rescue of determinism in the sense that the expected quantum stress tensor is generically singular on the Cauchy horizon. Furthermore, the strength of the singularity cannot be weakened by tuning the mass, charge and cosmological constant unlike in the classical theory. Thus, one can say that quantum theory saves determinism in this situation, rather than undermining it, as often proposed.

Abstract: Our understanding of quantum field theory is based on local observables (fields or algebras); but one seldomly considers how an actual measurement of these observables should be described consistently. In fact, when applying the usual recipes of quantum measurement theory – such as state update rules – in a relativistic context, one runs into contradictions: Certain combinations of measurements in space-time appear to lead to superluminal signalling (Sorkin, 1993). Hence how to exclude these “impossible measurements”? To settle this question, we analyse Sorkin’s signalling protocol in a measurement scheme for quantum field theory recently introduced by Fewster and Verch. Here a measurement of a relativistic system is described by coupling it to a probe, this coupling importantly being local in space and time. In this setting, we show that measurements do not exhibit superluminal signalling, and give a state update rule that is fully consistent with causality. In that sense, Sorkin’s impossible measurements can only be performed using impossible (namely non-local) apparatus.

Abstract: The D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite systems. It is shown that the D-CTC condition can generically be fulfilled in classical statistical systems, under very general, model-independent conditions. The central property used is the convexity and completeness of the state space that allows it to generalize Deutsch’s original proof for q-bit systems to more general classes of statistically described systems. The results demonstrate that the D-CTC condition, or the conditions under which it can be fulfilled, is not characteristic of, or dependent on, the quantum nature of a bi-partite system. This is joint work with Jürgen Tolksdorf.

Abstract: There is an ongoing debate whether the Reissner-Nordström-de Sitter spacetime, describing a spherically symmetric charged black hole on a de Sitter background, can be extended beyond the domain of dependence of the initial data, leading to a breakdown of determinism, or whether the slightest generic perturbation of the initial data would lead to the formation of a singularity at the “edge” of that domain, the Cauchy horizon. Recent results have shown that in some regime of the black hole charge and mass, classical scalar perturbations allow for an extension of the spacetime across the Cauchy horizon. In contrast to that, the stress-energy tensor of the quantum scalar field is divergent enough to lead to a singularity at the Cauchy horizon and save determinism, given that the coefficient of its leading divergence is non-zero. To calculate this coefficient, one needs to solve the Klein-Gordon equation for the massive scalar field in this spacetime. This is done semi-analytically. The results show that the coefficient is non-zero for generical spacetime parameters in the regime where classical perturbations allow for a breakdown of determinism.

Abstract: General relativity predicts that emission from near black holes will be lensed into a series of narrow “photon rings” converging to a critical curve on the image plane. I will describe the elegant analytic theory of this phenomenon and discuss a precise observational signature that could be measured with a dedicated space mission.

Abstract: In information theory one is interested in compressing information, of which only some part is relevant. Specifically, here we consider a quantum compression-decompression channel where sender and receiver share some side information. We compute the rate at which information can be sent through the channel so that the compressed signal retains a fixed amount of correlation with the side information, and find the optimum compression channel. Classically, this procedure was called the Bottleneck method, which we extend here to the quantum information domain.

Abstract: Interactions involving (massive) particles of spin >= 1 are often plagued by inconsistencies such as non-physical degrees of freedom and non-renormalizable due to the bad UV-behavior of higher-spin fields. These problems can already occur when a single field is coupled to an external potential. String-local fields can avoid such problems due to better UV-behavior and a fixed number of d.o.f. However, they have a worse localization in exchange and we have to proof that observables (scattering amplitudes etc.) are local quantities. In my master‘s thesis, I tried to tackle both issues at once. The idea is, to start with an inconsistent, non-renormalizable point-local Lagrangian, find a string-local Lagrangian without these problems and show that their S-matrices are (perturbatively) equivalent. While the string-local Lagrangian ensures renormalizability and consistency, the point-local Lagrangian proves locality of the S-matrix.

Abstract: A fundamental problem in the context of Einstein’s equations of general relativity is to understand precisely the dynamical evolution of small perturbations of stationary asymptotically flat spacetimes. It is expected that there is a discrete set of characteristic frequencies that play a dominant role at late time intervals and carry information about the nature of the stationary spacetime. These frequencies are called quasinormal frequencies and they are intimately related to resonances for Schrödinger equations. I will introduce a new method for characterizing quasinormal modes as honest eigenfunctions living in a Hilbert space, based on joint work with Claude Warnick.

Abstract: Fourier Integral Operators are a very versatile analytic tool, which has been used recently by Capoferri, Levitin and Vassiliev to construct the wave propagator on a closed Riemannian manifold M as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. In this talk, first of all we give a natural relativistic reinterpretation of this construction in the language of ultrastatic Lorentzian manifolds. Subsequently we show how the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario. Finally we outline how the overall procedure can be generalised to any globally hyperbolic spacetime with compact Cauchy surfaces. In the process we discuss the connections between our approach and the local Hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds. — Joint work with Matteo Capoferri (UCL & U. Cardiff) and Nicolò Drago (U. Würzburg), arXiv:2001.04164 [math.AP].

Abstract: The radiative dynamics in a gravitationally-bound two-body system with a small mass ratio can be described using a perturbative approach, whereby corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in the mass ratio, invoking the notion of “gravitational self-force”. The prospect of observing Extreme Mass Ratio Inspirals (EMRIs) with LISA has been motivating a program to obtain a rigorous formulation of the self-force and apply it numerically to describe the gravitational-wave signature of astrophysical EMRI systems. I will review the theory of gravitational self-force in curved spacetime, describe how this theory is being implemented in actual calculations, and discuss current status and open problems. I will highlight the way in which self-force calculations informs the development of other approaches to the two-body problem.

Abstract: The first objective of this talk will be to present the construction of non-interacting quantum fields on asymptotically anti-de Sitter spacetimes. The crucial ingredient is the holographic Hadamard condition, which ensures Hadamard behaviour in the space-time interior and existence of conformal fields induced at the boundary. In this setting I will explain how holography can be proved on the level of algebras of observables as a consequence of unique continuation theorems (based on joint works with Oran Gannot and Wojciech Dybalski).