Abstract

Killing-Yano symmetry has played an important role in the study of black hole physics since it was found that in the Kerr spacetime it allows separation of variables for the Hamilton-Jacobi, Klein-Gordon and Dirac equations. Due to the Killing-Yano symmetry, higher-dimensional vacuum black hole solutions possess similar integrability structure to the Kerr black hole.

In this talk, we discuss Killing-Yano symmetry of charged, rotating black hole solutions of the five-dimensional minimal supergravity as well as abelian heterotic supergravity. We will see that it leads us to introduce generalised Killing-Yano symmetry by considering skew-symmetric torsions which can be identified with matter fluxes in the theories. We also see that the generalised Killing-Yano symmetry shares almost identical properties with the standard one and implies the existence of important integrability structure for these black hole solutions. Moreover, we attempt to classify all metrics (which are not necessarily solutions of Einstein’s equation) admitting generalised Killing-Yano symmetry, which is expected to provide an ansatz for exact solutions of various supergravity theories.

Refs. arXiv:1004.1032, 1203.0393, 1212.2163 see also arXiv:1104.0852