Last week, I wrote an article entitled, “Can black holes reflect light?” in which we saw that a horizonless quantum blackhole (BH) called “fuzzballs”, reflect light. Now, Fabio Bacchini and colleagues studied the behavior of null geodesics (light rays) in four-dimensional fuzzball geometries and used this to obtained the first images of fuzzball shadows as they would be perceived by a distant observer.
They first constructed a novel axisymmetric scaling solution which they named the “ring fuzzball”. The ring fuzzball solution allows for the “scaling limit” λ → 0, in which it approaches the metric of the static, supersymmetric BH with
V = L_I = 0, K^I = 1 + 2P/r , M = − 1/2 + (P³ − q0)/ r
This BH has mass 2M_BH = 3P +q0−P³ and a horizon at r = 0 with area A_BH = 16π √P³(q0 − P³). The angular momentum of the (static) BH vanishes while the ring fuzzball has J = 2P³(1 − 3P²)λ. Note that this ring fuzzball represents the first ever explicitly constructed (exactly) scaling solution that is axisymmetric.
Thus, their analysis of this (axisymmetric scaling solution) confirms that, as far as the behavior of geodesics is concerned, fuzzballs in the scaling limit can resemble BH geometries arbitrarily well. It also reveals the key features and mechanisms of fuzzballs through which such phenomenological horizon behavior emerges.
The images presented in their paper are the first visualizations of fuzzball geometries. They confirmed several physical properties of microstate geometries which had generally been anticipated but never verified, such as their trapping behavior. They found that, as the ring fuzzball approaches the BH limit, its microstructure induces increasingly chaotic motion of geodesics (light-rays) straying in the near-center region. Infalling geodesics that reach the microstructure/fuzzball will be heavily blueshifted and subsequently backreact with the structure and/or be heavily scattered. The light that will emanate from this region will then be too redshifted to be detectable. In this way, the fuzzball/microstructure conspires to create a shadow very much like that of a BH, while avoiding the paradoxes associated with an event horizon.
You can see in fig 3, it clearly shows that, depending on the value of P, λ, fuzzballs can mimic black holes to different degree. In particular, fuzzball shadows can appear very dark, but with a much smaller area (top left); or, while the shadow size can be within observational uncertainty bounds, a weak redshift may make fuzzballs appear too bright (top right). With the appropriate parameters, fuzzballs can also appear indistinguishable from actual black holes (Bottom left)
Their results indicates that fuzzballs sufficiently near the scaling limit yield a theoretically appealing and phenomenologically viable BH alternative. Vice versa, observations of a faint residual glow in the object’s shadow, or of its shadow’s size compared to its mass, have the potential to discriminate between BHs and fuzzballs somewhat away from the scaling limit. These should therefore be prime targets for current and future imaging missions such as the EHT.
“Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects.“
— told Bacchini, first author of the study.
This motivates a more detailed investigation of the characteristics that differentiate fuzzballs from BHs through the intricate structure of their shadows. This will require not only further advances in the construction of more realistic fuzzballs but also an accurate modeling of the plasma in a realistic accretion disk, coupled to full radiative transfer methods. This approach has been employed for BH geometries considered by the EHT, as well as for more exotic objects, and researchers intend to report on this elsewhere.
More broadly, the chaotic behaviour of geodesics on the would-be horizon scales also suggested that gravitational waves propagating in this region will similarly be chaotically dispersed. Therefore one expects the resulting gravitational wave signal that leaks out to be chaotic and dispersed over extended time intervals. This suggested that the post-ringdown phase of gravitational waves generated in fuzzball mergers will not exhibit a markedly clear echo structure.
Reference: Fabio Bacchini, Daniel R. Mayerson, Bart Ripperda, Jordy Davelaar, Héctor Olivares, Thomas Hertog, Bert Vercnocke, “Fuzzball Shadows: Emergent Horizons from Microstructure”, pp. 1-6, ArXiv, 22 Mar 2021. https://arxiv.org/abs/2103.12075
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