Abstract
Quantum nature of black hole horizons has been a subject of recent interest and scrutiny. In particular, a near-horizon quantum violation of the equivalence principle has been proposed as a resolution of the black hole information paradox. Such a violation may lead to a modified dispersion relation at high energies, which could become relevant due to the intense gravitational blueshift experienced by ingoing gravitational waves. We investigate the ringdown for a perturbed black hole with such a modified dispersion relation and find that infalling gravitational waves are partially reflected near the horizon. This results in the appearance of late-time ${\it echoes}$ in the ringdown phase of black hole merger events, with similar properties to those (arguably) seen in the Advanced LIGO observations. Current measurements suggest a Lorentz-violation scale of $10^{13 \pm 2}$ GeV for gravitational waves, with comparable dissipation and dispersion. Therefore, if confirmed, black hole ringdown echoes probe the microstructure of horizons and thus can test Lorentz-violating UV completions, such as in Ho$\v{r}$ava-Lifshitz gravity.
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