Conformal Killing-Yano (CKY) symmetry has been studied as a fundamental hidden symmetry which plays a crucial role in black hole spacetimes. In this talk, after reviewing the history of CKY symmetry in four dimensions, I would like to present a generalization to higher dimensions and its applications. I further talk about CKY symmetry in the presence of skew-symmetric torsion. You will see that such a symmetry appears in black hole spacetimes of supergravity theories and that the torsion is naturally identified with a 3-form occuring in the theories. Finally, I would like to talk about recent progress if time permits. Ref. JHEP07(2010)055[arXiv:1004.1032]
I will introduce a simple idea how to define the volume of certain black holes, based entirely on thermodynamic considerations. I will present explicit expressions for the thermodynamic volume for a wide variety of black hole spacetimes and compare them with the "geometric volume" defined in previous studies. Finally, I will demonstrate that, at least phenomenologically, the thermodynamic volume seems to posses more universal properties. In particular, it seems to obey the reverse isoperometric inequality.
Recent years have seen a major progress in numerical relativity and the solution of the simplest and yet among the most challenging problems in classical general relativity: that of the evolution of two objects interacting only gravitationally. I will review the results obtained so far when modelling binaries of black holes or of neutron stars and also discuss the impact these studies have in detection of gravitational-waves, in astrophysics, and in our understanding of general relativity.
We consider the wave operator $\box_g=g^{ab}\nabla_a\nabla_b$ on Lorentzian manifolds where the metric $g$ is of low regularity. After recalling the classical theory of the wave equation on space-time we turn to the case of rough metrics. We present a local existence and uniqueness result for essentially bounded metrics based on the nonlinear distributional geometry in the sense of J.F. Colombeau. Finally, we extend this result to a global well-posedness theorem on (suitably generalized) globally hyperbolic space-times of low regularity.