Fuzzball Shadows: Emergent Horizons from Microstructure

We study the physical properties of four-dimensional, string-theoretical, horizonless “fuzzball” geometries by imaging their shadows. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon. 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.

Figure 1

From left to right columns: Visualizations of diagnostics for the ring fuzzball ($P=2$ and $q_0=50$) for decreasing values of $\lambda$, compared to the $\lambda \to 0$ 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 $M_{\mathrm{BH}}$); strongest redshift experienced by the geodesic (normalized to the redshift at the camera position); strongest curvature encountered (normalized to $K$ at the BH horizon).

Figure 2

Left panel: Three-dimensional visualization of a representative geodesic in the ring fuzzball geometry with $P=2,q_0=50$, and $\lambda =0.01$. The on-axis centers and the charged ring are shown in red. Right panels: A short portion (left column) and the full trajectory (right column) projected on the $\varphi =\pi /2$ plane, colored by elapsed time (top) and local redshift (bottom).

Figure 3

Visualization (see text) of ring fuzzballs with $P=1/4,\lambda =0.1$ (top left), $P=307/500,\lambda =0.3$ (top right), $P=7/8,\lambda =0.11$ (bottom left), compared to an extremal Kerr-Newman BH (bottom right) of equal mass (and same angular momentum as the bottom-left fuzzball). The two bottom pictures exhibit minimal but nonzero differences.