OCAMI International Workshop, March 16, 2015

Mathematics and Physics in General Relativity


March 16, 2015 @ Sugimoto campus of Osaka City University


Morning (Room E408) @@ Joint workshop with mathematics

09:30 - 10:20
Speaker: Claude Warnick (University of Warwick, UK)
Title: Symmetries and wave equations
Abstract: From a given Lorentzian manifold, the wave equation is the simplest geometric PDE one can construct. There is a close interplay between the geometry of the manifold and properties of the solutions of the wave equation. I will discuss how symmetries, hidden and otherwise, can be exploited to understand solutions of the wave equation, and I will present recent work concerning the stability of the anti-de Sitter spacetime.

10:30 - 11:20
Speaker: David Kubiznak (Perimeter Institute for Theoretical Physics, Canada)
Title: Dynamical symmetries in black hole spacetimes
Abstract: Starting from the well known Laplace-Runge-Lenz vector of the Kepler problem, I will introduce dynamical (hidden) symmetries as genuine phase space symmetries that stand in contract to the standard configuration space symmetries discussed by Noether's theorem. Proceeding to a relativistic description, I will demonstrate that such symmetries -- encoded in the so called Killing-Yano tensors -- play a crucial role in the study of rotating black holes described by the Kerr geometry. Even more remarkably, I will show that one such symmetry is enough to guarantee complete integrability of particle and light motion in general rotating black hole spacetimes in an arbitrary number of spacetime dimensions. Some further developments in the area of Killing-Yano tensors will also be discussed.

11:30 - 12:20
Speaker: Yoshitake HashimotoiTokyo City University & Visiting Professor of OCAMI, Japan)
Title: Conformal field theory on stable curves
Abstract: (joint work with Akihiro Tsuchiya) Conformal field theory is a quantum field theory with conformal symmetry on 2-dimensional spacetime with singularity. In this theory fields of operators constitute an "algebra" with regularization for avoiding divergence in product of operators, which is called vertex algebra. Mechanism of regularization is closely related to degeneration of Riemann surfaces. I will discuss a relation between field theory on families of Riemann surfaces with degeneration and representation theory of vertex algebras, especially tensor structure in the categories of the representations, which is related to quantum groups.

Afternoon (Room E108)

14:00 - 14:30
Speaker: Chulmoon Yoo (Nagoya University, Japan)
Title: Simulating periodic nonlinear inhomogeneity with numerical relativity
Abstract: We report our recent works on numerical simulations of lattice universe models. First, we report initial data construction and time evolution of the "black hole universe". The black hole universe is a solution of the vacuum Einstein equations composed of periodically aligned black holes. We show that evolution of an effective scale factor is well approximated by that in the Einstein-deSitter universe. The black hole universe with positive cosmological constant is also simulated. We show its structure focusing on the evolution of configuration of marginally trapped surfaces. Finally, we report recent results on the ``gravitational wave universe" which is composed of periodic non-linear gravitational standing waves.

14:30 - 15:00
Speaker: Keiju Murata (Keio University, Japan)
Title: Turbulent strings in AdS/CFT
Abstract: We study nonlinear dynamics on the flux tube between an external quark-antiquark pair in N=4 super Yang-Mills theory using the AdS/CFT duality. In the gravity side, the quark-antiquark pair is realized by a fundamental string whose endpoints are attached on the AdS boundary. We numerically compute the time evolution of the string with motions induced by perturbing the endpoints. Cusps can form on the string as a result, accompanied by weak turbulence and power law behavior in the energy spectrum. When a cusp traveling on the string reaches the boundary, we observe divergence of the force acting between the quark and antiquark. Minimal amplitude of the perturbation below which cusps do not form are also investigated. No cusp formation is found when the string moves in all four AdS space directions, and in this case an inverse energy cascade follows a direct cascade.

(30min break)

15:30 - 16:00
Speaker: Hiromi Saida (Daido University, Japan)
Title: Toward a specification of strong gravity region by unstable confined orbits of null particles
Abstract: How can we specify a region governed by strong gravity? The inside of black hole region, or the so-called trapped region, may be usually regarded as a good definition of strong gravity region. However, when an observer at infinity (with assuming asymptotic flatness for simplicity) tries to observe such a strong gravity region, it is impossible for the observer to detect photons which come from the surface of black hole or trapped region. A strong gravity region defined as the inside of BH or trapped region seems to be undetectable by outside observers. In this talk, I want to discuss how can we define a strong gravity region so as to be detectable by outside observers. Currently, I am considering to make use of the notion of unstable circular orbit of photons in Schwarzschild spacetime. Its counter-part in Kerr spacetime is not a circle but a curve confined on a shell of constant radius around Kerr BH. In black hole spacetimes, a strong gravity region which is detectable by outside observers may be defined as the region surrounded by Unstable Confined Orbits of Photons (null-mass particles), UCOP. A problem is how the notion of UCOP is extended to a more general (low symmetric, dynamical) spacetimes.

16:00 - 16:30
Speaker: Tsuyoshi Houri (Kobe University, Japan)
Title: Some spacetimes with higher rank Killing-Stackel tensors
Abstract: I will discuss some spacetimes with higher rank Killing-Stackel tensors, where Hamilton-Jacobi equations for geodesics cannot be solved by separation of variables, but integrable in the Liouville sense.

(30min break)

17:00 - 17:30
Speaker: Ryotaku Suzuki (OCAMI, Japan)
Title: Classical dynamics of the black hole horizon in the large D limit
Abstract: Recently, black hole/objects in sufficiently large number of dimension, namely in the large D limit, are found to have much simpler structure. In this limit, the near horizon structure of any neutral black hole resembles that of the Schwarzschild black holes, even with the rotation. Since the near horizon equation also decouples from the far region in the limit, the horizon deformation dynamics can be treated in the unified manner independent of the global geometry. In this talk, recent results of the large D limit are discussed.

17:30 - 18:00
Speaker: Hideki Ishihara (Osaka City University, Japan)
Title: Symmetry of an orbit space of the isometry group acting on the sphere
Abstract: We consider an orbit space of the isometry group action generated by a Killing vector on a space, and introduce a metric that is weighted by the norm of the Killing vector. In the case of n-dimensional sphere, we classify the orbit spaces, and show the Hamiltonian system of the geodesic on the all orbit spaces are integrable in the Liouville sense, i.e., there exists n Poisson commuting invariants, with the help of the existence of Killing tensors. On a view point of physics, it suggests that the cohomogeniety-one Nambu-Goto strings in (anti-) de Sitter space are integrable.


Osaka City University Advanced Mathematical Institute
3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka, 558-8585 Japan


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