Gravitational-wave echoes from spinning exotic compact objects: numerical waveforms from the Teukolsky equation

TL;DR

This paper numerically models gravitational-wave echoes from spinning exotic compact objects by solving the Teukolsky equation, providing more realistic waveforms that account for ECO surface reflections and Kerr spacetime effects.

Contribution

It introduces a novel numerical approach to generate gravitational-wave echoes from spinning ECOs using the Teukolsky equation and membrane paradigm boundary conditions.

Findings

Echoes are significantly weaker than previous models.

Waveforms closely match those from comparable-mass black hole mergers.

Refined modeling improves understanding of ECO gravitational-wave signatures.

Abstract

We present numerical waveforms of gravitational-wave echoes from spinning exotic compact objects (ECOs) that result from binary black hole coalescence. We obtain these echoes by solving the Teukolsky equation for the $\psi_4$ associated with gravitational waves that propagate toward the horizon of a Kerr spacetime, and process the subsequent reflections of the horizon-going wave by the surface of the ECO, which lies right above the Kerr horizon. The trajectories of the infalling objects are modified from Kerr geodesics, such that the gravitational waves propagating toward future null infinity match those from merging black holes with comparable masses. In this way, the corresponding echoes approximate to those from comparable-mass mergers. For boundary conditions at the ECO surface, we adopt recent work using the membrane paradigm, which relates $\psi_0$ associated with the horizon-going wave and $\psi_4$ of the wave that leaves the ECO surface. We obtain $\psi_0$ of the horizon-going wave from $\psi_4$ using the Teukolsky-Starobinsky relation. The echoes we obtain turn out to be significantly weaker than those from previous studies that generate echo waveforms by modeling the ringdown part of binary black hole coalescence waveforms as originating from the past horizon.