Claude M. Warnick

Stationary metrics and optical Zermelo-Randers-Finsler geometry

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Fins- lerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalisation of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various is- sues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo-surface in the spacetime picture. The gauge equivalence in this network of rela- tions is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.

On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes

We consider the problem of quasinormal modes (QNM) for strongly hyperbolic systems on stationary, asymptotically anti-de Sitter black holes, with very general boundary conditions at infinity. We argue that for a time slicing regular at the horizon the QNM should be identified with certain Hk eigenvalues of the infinitesimal generator

Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes

{\mathcal{A}}

Light bending in Schwarzschild–de Sitter: projective geometry of the optical metric

A of the solution semigroup. Using this definition we are able to prove directly that the quasinormal frequencies form a discrete, countable subset of

Some spacetimes with higher rank Killing―Stäckel tensors

{\mathbb{C}}

Local metrics admitting a principal Killing-Yano tensor with torsion

C which in the globally stationary case accumulates only at infinity. We avoid any need for meromorphic extension, and the quasinormal modes are honest eigenfunctions of an operator on a Hilbert space. Our results apply to any of the linear fields usually considered (Klein- Gordon, Maxwell, Dirac, etc.) on a stationary black hole background, and do not rely on any separability or analyticity properties of the metric. Our methods and results largely extend to the locally stationary case. We provide a counter-example to the conjecture that quasinormal modes are complete. We relate our approach directly to the approach via meromorphic continuation.