Amplification of gravitational wave by a Kerr black hole

Binary black hole (BH) may form near a supermassive black hole. The background 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.