Bulk-cone singularities and echoes from AdS exotic compact objects

TL;DR

This work shows how AdS/CFT can access regions inside the photon sphere of ECOs, predicting two hallmark signatures in boundary correlation functions: bulk-cone singularities tied to bulk null geodesics and echoes from modes trapped within the photon sphere. By combining geodesic analyses, WKB wave methods, and numerical computations, the authors demonstrate these signatures for AdS gravastars and AdS thin-shell wormholes, extending previous results beyond AdS-Schwarzschild BHs. The findings provide a concrete, holographic diagnostic to distinguish BHs from ECOs and reveal how interior geometry imprints appear in boundary observables, with implications for Lyapunov exponents, decay rates, and potential CFT interpretations of ECO instabilities. The methodology and results offer a versatile framework for probing interior spacetime structures in holographic settings and motivate further exploration of more realistic ECO models.

Abstract

The region near a black hole horizon may be modified by quantum gravity effects that resolve the singularity. Such geometry may be represented by an exotic compact object. Because the horizon is enclosed by a photon sphere, it is difficult to probe this region directly. In this paper, we develop a method to study the region inside the photon sphere by applying the AdS/CFT correspondence. We extract signatures of the modified geometry from the retarded Green functions of the dual conformal field theory. The retarded Green functions can be computed from bulk wave functions of scalar field. We show that exotic compact objects leave two characteristic imprints: bulk-cone singularities and echoes. The bulk-cone singularities correspond to null geodesics in the bulk, allowing us to detect null trajectories that are specific to exotic compact objects. The echoes arise from wave modes trapped inside the photon sphere, and thus signal the absence of a horizon. As concrete examples, we study AdS gravastar and AdS wormhole. We compute the corresponding bulk wave functions both via the WKB approximation and through numerical analysis and observe the bulk-cone singularities and echoes explicitly.

Figures (35)

• Figure 1: The shape of potential for the null geodesic in AdS-Schwarzschild black hole.
• Figure 2: Illustration of null geodesics connecting two points on the boundary of AdS Schwarzschild black hole. The left trajectory $\mathrm{BC}_{0+}^1$ with $\theta=\pi/2$ has the angular displacement $2\pi j+\theta=5\pi/2$ with no bounce ($n-1=0$) at the boundary. The right trajectory $\mathrm{BC}_{1+}^1$ has the same displacement $2\pi j+\theta=5\pi/2$ with $n-1=1$ bounce. They wind around the photon sphere radius (the red circle).
• Figure 3: The bulk-cone structure for AdS-Schwarzschild black hole with $d=3$, $\mu=1/15$ (left) and $d=4$, $\mu=1/50$ (right). The retarded Green function $G_\mathrm{R}(t,\theta)$ is divergent along the red curves. It is also divergent along the gray lines corresponding to the light-cone singularity.
• Figure 4: The potential for AdS-Schwarzschild black hole.
• Figure 5: The potential for AdS gravastar as a typical example of ECOs.