Amplification of gravitational wave by a Kerr black hole

TL;DR

This paper investigates how a Kerr black hole background can amplify or suppress gravitational wave energy emitted by a nearby binary black hole, finding that relative motion is key to energy amplification.

Contribution

It is the first to compare gravitational wave energies with and without a Kerr black hole background, revealing amplification only occurs with relative motion.

Findings

GW energy can be amplified up to 5 times by a Kerr black hole background.

Amplification occurs only when the binary black hole moves relative to the Kerr black hole.

Energy is suppressed if there is no relative motion between the binary and the Kerr black hole.

Abstract

Binary black hole may form near a supermassive black hole. The background black hole (BH) will affect the gravitational wave (GW) generated by the binary black hole. It is well known that the Penrose process may provide extra energy due to the ergosphere. In the present paper we investigate the energy amplification of the gravitational wave by a Kerr black hole background. In particular and different from the earlier studies, we compare the energies of the waves in the cases with and without a nearby Kerr BH. We find that only when the binary black hole is moving relative to the Kerr background can the GW energy be amplified. Otherwise, the energy will be suppressed by the background Kerr black hole. This finding is consistent with the inequality found by Wald for Penrose process. Taking into account realistic astrophysical scenarios, we find that the Kerr black hole background can amplify the GW energy by at most 5 times.