Lifshitz scaling, ringing black holes, and superradiance

TL;DR

This paper explores how Lifshitz scalar fields around Schwarzschild black holes exhibit unique ringdown waveforms, superradiance, and long-lived quasinormal modes due to Lorentz-breaking effects, significantly affecting black hole radiation properties.

Contribution

It introduces the study of Lifshitz scalar fields' wave dynamics around black holes, revealing new phenomena like superradiance and long-lived modes caused by Lorentz-breaking terms.

Findings

Lifshitz waves show diverse ringdown waveforms.

Superradiance occurs for Lifshitz waves scattered by black holes.

Long-lived quasinormal modes emerge with roton-like dispersion.

Abstract

We investigate the ringdown waveform and reflectivity of a Lifshitz scalar field around a fixed Schwarzschild black hole. The radial wave equation is modified due to the Lorentz breaking terms, which leads to a diversity of ringdown waveforms. Also, it turns out that Lifshitz waves scattered by the Schwarzschild black hole exhibits superradiance. The Lorentz breaking terms lead to superluminal propagation and high-frequency modes can enter and leave the interior of the Killing horizon where negativity of energy is not prohibited. This allows the Lifshitz waves to carry out additional positive energy to infinity while leaving negative energy inside the Killing horizon, similar to the Penrose process in the ergosphere of a Kerr spacetime. Another interesting phenomenon is emergence of long-lived quasinormal modes, associated with roton-type dispersion relations. These effects drastically modify the greybody factor of a microscopic black hole, whose Hawking temperature is comparable with or higher than the Lifshitz energy scale.