How Would Be Fuzzballs Shadow? (Quantum / Astronomy / Cosmology)

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.

FIG. 1: From left to right columns: visualizations of diagnostics for the ring fuzzball (P = 2 and q0 = 50) for decreasing values of λ, compared to the λ → 0 BH in the rightmost column. Rows from top to bottom: four-color screen indicating the portion of the celestial sphere from which geodesics originate; coordinate time t elapsed at the end of the numerical integration (normalized to MBH); strongest redshift experienced by the geodesic (normalized to the redshift at the camera position); strongest curvature encountered (normalized to K at the BH horizon). © Bacchini et al.

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.

FIG. 2: Left panel: three-dimensional visualization of a representative geodesic in the near-center region of the ring fuzzball geometry with P = 2, q0 = 50 and λ = 0.01. The on-axis centers and the charged ring are shown in red. Middle column: a short portion of the same trajectory projected on the φ = π/2 plane, colored by elapsed time (top) an local redshift (bottom). Right column: the full chaotic trajectory shown until the final integration time. © Bacchini et al.
FIG. 3: Visualization of ring fuzzballs with P = 1/4, λ = 0.1 (top left), P = 307/500, λ = 0.3 (top right), P = 7/8, λ = 0.11 (bottom left), compared to an extremal Kerr-Newman BH (bottom right) of equal mass (and same angular momentum as the bottom left fuzzball). All images are darkened according to the maximal redshift encountered by each geodesic. The two bottom pictures exhibit minimal but non-zero differences. © Bacchini et al.

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.

Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us

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