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Conformal Klein-Gordon equations and quasinormal modes

Roldao da Rocha·E. Capelas de Oliveira
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Abstract

Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal radial d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this radial equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.

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Roldao da Rocha, E. Capelas de Oliveira. 2006-03-20. Conformal Klein-Gordon equations and quasinormal modes. https://doi.org/10.1007/s10773-006-9238-5

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