Is the gravitational-wave ringdown a probe of the event horizon?

TL;DR

It is pointed out that this assumption that very compact objects with a light ring will display a similar ringdown stage, even when their quasinormal-mode spectrum is completely different from that of a black hole, is wrong.

Abstract

It is commonly believed that the ringdown signal from a binary coalescence provides a conclusive proof for the formation of an event horizon after the merger. This expectation is based on the assumption that the ringdown waveform at intermediate times is dominated by the quasinormal modes of the final object. We point out that this assumption should be taken with great care, and that very compact objects with a light ring will display a similar ringdown stage, even when their quasinormal-mode spectrum is completely different from that of a black hole. In other words, universal ringdown waveforms indicate the presence of light rings, rather than of horizons. Only precision observations of the late-time ringdown signal, where the differences in the quasinormal-mode spectrum eventually show up, can be used to rule out exotic alternatives to black holes and to test quantum effects at the horizon scale.

Figures (4)

• Figure 1: Illustration of a dynamical process involving a compact horizonless object. A point particle plunges radially (red dashed curve) in a wormhole spacetime, and emerges in another "universe". The black curve denotes the wormhole's throat, the two gray curves are the light rings. When the particle crosses each of these curves, it excites characteristic modes which are trapped between the light-ring potential wells, see Figs. \ref{['fig:potential']} and \ref{['fig:ringdown']}.
• Figure 2: The first three tones $(n=0,1,2$) for the two families of polar $l=2$ QNMs of a wormhole parametrically shown in the complex plane for different values of the throat location $r_0$, and compared to the first QNMs of a Schwarzschild BH. In the BH limit ($r_0\to 2M$) all QNMs of the wormhole approach the real axis.
• Figure 3: Effective ($l=2$) potential in tortoise coordinates for a static traversable wormhole (top panel) with $r_0=2.001M$ and for a Schwarzschild BH (bottom panel).
• Figure 4: Left panels: quadrupolar GW energy spectrum [cf. Eq. \ref{['dEdw']}] for a point particle crossing a traversable wormhole and compared to the case of a particle plunging into a Schwarzschild BH with the same energy $E$. Top and bottom panels refer to $r_0=2.1M$, $E=1.1$ and to $r_0=2.001M$, $E=1.5$, respectively (different parameters give qualitatively similar results). Vertical dashed lines denote the frequency of the first QNMs of the wormhole (cf. Fig. \ref{['fig:QNMs']}) which correspond to narrow resonances in the flux Pons:2001xsBerti:2009wx. Right panels: the corresponding GW waveforms compared to the BH case. The BH waveform was shifted in time by $\Delta t$ [cf. Eq. \ref{['Deltat']}] to account for the dephasing due to the light travel time from the throat to the light ring.