discussion

Empirical evidence for \(\Upsilon > 0\):
Echoes from the abyss

One of the predictions of GET for the choice \(\Upsilon > 0\) is that there will be no black holes, but, instead, stable gravastars or frozen stars with extreme surface time dilation. For sufficiently small \(\Upsilon \ll 1\) the surface time dilation becomes arbitrary large. Given that the expansion of the universe gives already a quite strong upper bound for \(\Upsilon\) (because the big bounce has to happen before the background radiation has been created) the differences between the GR black hole solution and the GLET frozen star solution will be very small even very close to the surface of the frozen star.

In other alternative theories where quantum gravity effects lead to gravastars, the radius of the gravastar is expected to be a Planck length greater than the horizon. In GLET, this radius has no connection with Planck length, but is defined by \(\Upsilon\). For small enough \(\Upsilon\) it will be even less than Planck length. So, it seems clear that essentially nothing will be visible on the surface.

Nonetheless, there has been the prediction that the existence of a surface leads to observable effects during the merger of two black holes, and that these effects will be large enough to be observable:

As first noticed in [18, 19], introduction of structure near event horizon leads to late, repeating, echoes of the ringdown phase of the black hole merger, due to waves trapped between the near-horizon structure and the angular momentum barrier (Fig. 1). [1]

Given that most of the region between the surface and the angular momentum barrier is in a region where the GLET solution will be indistinguishable from the GR solution, these computations will be applicable to GLET at least this part too. The only part which could reasonably be questioned would be if the quite general argumentation that the surface acts as a mirror is correct:

This picture is motivated by the realization that a thermal membrane on the stretched horizon, satisfying Israel junction conditions with \(\mathbb{Z}_2\) symmetry, happens to have a thermal entropy equal to the Bekenstein-Hawking area law [13]. Therefore, any horizonless microscopic model of the black hole which accounts for its entropy, should act as a mirror, at least for linear long wavelength perturbations. The mirror is not perfect for particles with \(\omega \gg T_H\) (= Hawking temperature), as they can excite the microstates of the system, and thus be absorbed by the membrane [14], but should be reflective at \(\omega \lesssim T_H\) as these microstates cannot be excited. Incidentally, this is the frequency regime for gravitational waves in the ringdown phase of black hole mergers. In contrast, electromagnetic emissions from accretion into black holes are at much higher frequencies, where the membrane is expected to be highly absorbing, consistent with astrophysical observations [15, 16] (but also see [11, 17]). [1]

This argument sounds sufficiently plausible, so that I would expect that such echoes would be predicted by GLET too.

Evidence from the black hole mergers

Abedi, Dykaar and Afshordi have tried to find such echoes in the data from the black hole mergers detected by LIGO, and it appears that already this first observations have given some evidence for such echoes:

Quite surprisingly, we find statistical evidence for these delayed echoes in LIGO events: GW150914, GW151226, and LVT151012 at a combined significance of \(2.9\sigma\). [1]

Of course, it would be unreasonable to expect that already these first events give some definite answer. There is a discussion about the question what the data already give, and I prefer not to argue about who is right, and prefer to wait for more data.

Nonetheless, up to now there is at least some evidence that the GLET prediction is correct.

References:

  1. J. Abedi, H. Dykaar, N. Afshordi, Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons, arXiv:1612.00266
  2. G. Ashton et al., Comments on: "Echoes from the abyss: Evidence for Planck-scale structure at black hole horizons", arXiv:1612.05625
  3. J. Abedi, H. Dykaar, N. Afshordi, Echoes from the Abyss: The Holiday Edition!, arXiv:1701.03485