Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry

TL;DR

This paper investigates the application of connection formulae in Lifshitz geometry to black hole perturbations, focusing on the collision limit where singularities merge, and provides evidence supporting this approach.

Contribution

It explores the feasibility of taking the collision limit of connection formulae in Lifshitz geometry, a novel approach in black hole perturbation analysis.

Findings

Supportive evidence for the collision limit in connection formulae

Potential for computing quasinormal modes and Green functions

Extension of connection formulae applicability in Lifshitz backgrounds

Abstract

The connection formulae provide a systematic way to compute physical quantities, such as the quasinormal modes, Green functions, in blackhole perturbation theories. In this work, we test whether it is possible to consistently take the collision limit, which bring two or more regular singularities into an irregular one, of the connection formulae, and we provide some supportive evidence for it.