Lifshitz scaling, ringing black holes, and superradiance

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 exhibit 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.

Automated summary

This study investigates the ringdown waveform and reflectivity of a Lifshitz scalar field around a fixed Schwarzschild black hole, finding that Lifshitz waves scattered by the black hole exhibit superradiance due to Lorentz breaking terms leading to superluminal propagation. This can allow Lifshitz waves to carry additional positive energy to infinity while leaving negative energy inside the Killing horizon, similar to the Penrose process in Kerr spacetime. The study also observes the emergence of long-lived quasinormal modes and drastic modifications to the greybody factor of a microscopic black hole with Hawking temperature comparable to the Lifshitz energy scale.