Title: Price's law for Teukolsky master equation in Kerr spacetimes
Abstract: Teukolsky master equation governs the dynamics of the spin $s$ components in Kerr spacetimes. I will show their precise late time asymptotic profiles, i.e., the conjectured Price's law in the physics literature.
Title: An introduction to spinor and twistor methods for gravitation
Abstract: We give an elementary introduction to spinors in 4 complex dimensions, focusing on the different reality structures associated with Lorentzian and Riemannian signatures. We discuss connections with almost-complex structures and with integrability aspects relevant to gravitation, especially regarding algebraically special geometries. The emphasis is on a pedagogical presentation; no previous knowledge of spinors or complex geometry is assumed.
Titel: Belinski-Zakharov method revisited
Abstract: The Belinski-Zakharov (BZ) method is among the various solution generating techniques for 4-dimensional, Ricci flat metrics with two Killing vectors. It was used by Chen and Teo to find a new asymptotically flat gravitational instanton solution. In this talk we review the BZ method and conjecture a simple combinatorical form for the generated metrics.
Titel: G-to-zero limit of Kerr-Newman solution
Abstract: The limit of vanishing G of the maximal analytically extended Kerr–Newman solution in Boyer–Lindquist coordinates leads to the so-called 'magic electromagnetic field' (or the square root of Kerr) on a topologically nontrivial flat spacetime. The background, in this case, is a two-sheeted spacetime with special leaves represented in oblate spheroidal coordinates. The magic electromagnetic field can also be generated by a complex shift in the Coulomb field, parallel to the Newman and Janis transformation. I will review some of the interesting questions and results along these lines.
Titel:On $S^1$-symmetric gravitatonal instantons
Abstract: Gravitational instantons are complete 4-dimensional Ricci-flat manifolds with Riemannian signature and curvature decaying sufficiently fast. I shall present ongoing work on the classification of $S^1$-symmetric gravitational instantons. The approach taken makes use the $G$-signature theorem and an identity of Israel-Robinson type.
(University of Vienna)
Titel: Spin Hall effects and gravitational lensing
Abstract: Spin Hall effects represent a diverse class of physical phenomena related to the propagation of wave packets carrying intrinsic angular momentum. These effects have been experimentally observed in optics and condensed matter physics, but they are also expected to occur for wave packets propagating in gravitational fields. In this talk, I will introduce the equations of motion describing the gravitational spin Hall effect, and I will discuss their properties, physical interpretation, as well as the relation to the Mathisson-Papapetrou equations. Based on this, I will present recent results regarding the strong lensing of gravitational waves. Given the typical wavelengths of observed gravitational waves, the gravitational spin Hall effect is expected to have a significant effect that could lead to experimental observation.
(Jagiellonian University, Krakow)
Titel: Bound states of nonlinear Schrödinger equations with trapping potentials in higher dimensions
Abstract: In this talk I would like to discuss some results regarding a particular nonlinear Schrödinger equation, dubbed by us the Schrödinger-Newton-Hooke equation. It is usually encountered as a description of various quantum-mechanical systems but it can also be obtained as a nonrelativistic limit of small scalar perturbations of the anti-de Sitter spacetime. This observation gives us a motivation to investigate this equation in higher dimensions. However, it turns out that for dimensions d>6 not very much is known about it, since the usually employed approach based on the variational methods ceases to work. I would like to show how one can overcome this problem by focusing on spherically symmetric solutions and using the classical methods coming from the field of ordinary differential equations. In particular, I will prove the existence of the whole ladder of excited solutions and show the uniqueness of the ground states. I will also discuss how the frequencies and masses of the solutions vary for different dimensions. Most of the presented methods and results hold also for other similar systems with trapping potentials.
Titel: Electromagnetic and gravitational Hopfions
Abstract: Hopfions are a family of field solutions which have non-trivial topological structure. Their connections with Hopf fibration will be presented. I will focus on two physical applications of Hopfions: electromagnetism and linear gravitation. The issue of topological charges will be briefly discussed.
(Universidad de la República, Montevideo, Uruguay)
Titel: Numerical Studies of Axisymmetric Periodic Analogues of Kerr Black Holes
Abstract: In this talk we present some results concerning the numerical study of solutions to the axisymmetric stationary Einstein Equations in a coaxial periodic set up. Since the discovery of the periodic static solutions by Myers, and independently by Korotkin and Nicolai, the existence of solutions in the stationary case has been elusive, for one particular reason: the kind of asymptotic behaviour of the solutions implies the divergence in the usual barrier methods used to prove existence. We adopt a numerical approach, working with two possible configurations: one with equidistant horizons with the same angular momentum, and one with equidistant horizons with alternating opposite angular momentum. The parameters are the period and the length, area and angular momentum of the horizons. We will show how the numerical implementation is done via a harmonic map heat flow, and the introduction of new boundary conditions that are suitable for the problem will be discussed. Finally, we will show the results we obtained.
Titel: On black holes and Buchdahl stars
Abstract: Buchdahl star is the most compact non black hole object, and the two are respectively defined by gravitational potential, $\Phi(R) = 4/9, 1/2$. We would first argue that the Buchdahl star is a Virial distribution where its equilibrium is due to the Virial theorem, and then attempt to see what kind of black hole properties like extremalization and over extremalization could be carried over to the Buchdahl star. Could Buchdahl star serve as a precursor to black hole, and in particular its role in formation of extremal black holes.
Titel: Kähler geometry, black holes, and twistor integrals
Abstract: Using complex methods in relativity, we show that black hole geometries can be encoded in a single scalar function, called Kähler potential. We show that this function encodes the Newman-Janis shift from Schwarzschild to Kerr, as well as different dualities within the Plebanski-Demianski family of solutions. At the linear level, we show that these structures can be nicely understood in terms of twistor theory. This is joint work with Steffen Aksteiner.
Titel: Graviton amplitudes from twistor sigma models
Abstract: I will discuss a new tool that helps us obtain Andrew Hodges' extremely compact formulae for tree-level graviton MHV amplitudes in GR. Unlike previous on-shell methods like recursion or worldsheet models, our approach starts directly from space-time perturbation theory. It systematically constructs a generating functional for these MHV amplitudes by means of hyperkähler geometry and twistor theory. This generating functional takes the form of the on-shell action of a 2d defect CFT that we call a twistor sigma model. We show how computing this on-shell action results in a tree-diagram expansion of the MHV amplitudes anticipated by Bern, et al in 1998. The diagrams, when resummed via the matrix tree theorem, magically condense into Hodges' formulae. Time permitting, I will also comment on a flat holographic interpretation of the twistor sigma model.
(University of Potsdam)
Titel: On the index theorem and the Rokhlin theorem