Quasinormal Modes in Near-Extremal Spinning C-Metric

TL;DR

This paper analytically studies the quasinormal modes of a spinning C-metric spacetime with a conformally coupled scalar field, revealing how the near-extremal limit simplifies the potential to a P"{o}shl-Teller form and quantizes decay rates.

Contribution

It provides the first analytical derivation of quasinormal frequencies for the near-extremal spinning C-metric with a conformally coupled scalar field.

Findings

Potential reduces to P"{o}shl-Teller form near extremality

Decay rates are quantized in the near-extremal limit

Analytical expressions for quasinormal frequencies are obtained

Abstract

We investigate the quasinormal modes of the spinning C-metric with a massless scalar field conformally coupled with gravity. Conformal transformation is employed to separate and subsequently solve the massless scalar field equations. As the outer and acceleration horizons approach each other, the potential term of the field equation is reduced to the P\"{o}shl-Teller potential because the acceleration horizon is similar to the cosmological horizon of de Sitter spacetime. Finally, we obtain the analytical quasinormal frequency at which the decay rate is quantized.