Current seminars

Abstract: I will present a method of determining the mass density along the line of sight using variations of times of arrival of electromagnetic signals, as measured by two ensembles of free falling, precise clocks. The whole set-up may be considered a type of an extended gravitational compass, i.e. a device measuring directly the spacetime curvature using an ensemble of communicating clocks. I will also discuss the geometric interpretation of this measurement.

Abstract: Linear perturbations of black holes have been discussed widely in many contexts. Of interest are properties such as differential cross-sections or quasi-normal modes. A useful tool in this respect is the Newman-Penrose formalism and the resulting Teukolsky equations, giving seperated angular and radial differential equations. These were mostly evaluated by numerical means or in approximations. However, the introduction of a cosmological constant allows the problem to be solved in an exact analytical manner by transforming the differential equations into the Heun differential equation, the most general second-order differential equation with four regular singularities. We show for the Kerr-de Sitter spacetime that scattering of waves from a point source needs an additational discussion around the so-called Heuns function, which enables a then possible normalization of the angular solution, similarly to the case of spherical harmonics. We assume in the discussion and analysis a scalar source star of fixed frequency and solve the scattering problem by a partial wave sum. The observed wave optical image formation by means of Kirchhoff-Fresnel diffraction and the resulting shadow will be compared to e.g. the ray-optical black hole shadow.

Abstract: In this talk, I will describe recent and upcoming work on the asymptotic behaviour of gravitational radiation (linearised gravity around Schwarzschild) in a neighbourhood of spacelike infinity including past and future null infinity. I will first set up a mathematical scattering framework in which one can understand the question of smoothness of null infinity on physical grounds. I will then use this framework to present a basic sketch of the proof of the irregularity of null infinity in various physically motivated settings, together with a complete description of the semiglobal asymptotics of gravitational radiation one obtains instead. In particular, I will discuss how a class of asymptotic conservation laws related to the Newman-Penrose charges can be used to infer the asymptotics for fixed angular modes, and describe how to use a persistence of polyhomogeneity result to sum up the individual angular modes. Based on joint work with Hamed Masaood and Istvan Kadar.

Abstract: In this talk I will show that there are vacuum static 3+1 black hole solutions, metrically complete but non-standard spatial topology, that cannot be put into stationary rotation. That is, there are no non-static stationary metrics close to them. To our knowledge, this is the first result of this kind in the literature. This is joint work with Javier Peraza.

Abstract: One is probably aware that classification of RCFTs has been studied at a steady and formal pace over the past few decades. But often when we are asked to define or characterize an RCFT who target spaces are X, there are different answers and characterisations. (X can be an abelian variety like a torus, or a an algebraic variety like K3 surfaces etc.) Phenomenologically, rationality can explain things like electroweak gaugino dark matter, gauge coupling unification and small gravitino mass, and attribute them to large chiral algebra on the worldsheet string theory, and not to a larger symmetry of the spacetime field theory. Mathematically, Rational CFTs provide a physical way to determine points of arithmetic in the moduli space of a variety. For the case of X = d dimensional tori, these various characterisations as I will explain are equivalent if and only if there are further conditions imposed and provide a sketch of proof. I will also discuss possible connections to random matrix theories and arithmetic of abelian varieties if time permits.

Abstract: Isolated gravitational systems such as stars, galaxies and black holes are modeled by asymptotically flat initial data sets. In 1981 Schoen-Yau and Witten showed that such initial data sets with vanishing energy must be contained in Minkowski space. We show that if such initial data sets have vanishing mass, they must be contained in pp-wave spacetimes. This is based upon joint work with Yiyue Zhang from UCI.