Poincaré asymptotic expansion in black hole theory

In studying the dynamics of fields in black hole theory, the method of separation of variables makes it possible to isolate the radial part of the full solution in many important physical cases. This occurs by virtue of the existence of the principal tensor in Petrov-D metrics. We first review this mathematical result in order to introduce several cases where it is possible to study the radial solution via the Poincaré asymptotic series expansion, a tool exploited in recent work by the authors in order to investigate the behaviour of the field at spacelike infinity, a point in the neighbourhood of which only approximate solutions are computable by virtue of its irregular nature. We obtain a series which can be computed to any degree of accuracy, allowing for a deeper analysis of this challenging spacetime region. An application to quasinormal modes is eventually provided.