Light trajectories and optical appearances in asymptotically Anti-de Sitter-Schwarzschild and black string space-times

TL;DR

This work investigates how light propagates and images form around compact objects embedded in asymptotically Anti-de Sitter spacetimes, focusing on Schwarzschild-AdS black holes and black strings. By deriving null geodesics, defining a transfer-function framework, and modeling simplified disk emission, the authors analyze how AdS asymptotics alter photon spheres, critical impact parameters, and the resulting direct and photon-ring structures in observer images. They find that Schwarzschild-AdS behaves similarly to its asymptotically flat counterpart but with a nonvanishing potential at infinity, modifying the transfer functions and image brightness; black strings exhibit more pronounced departures due to cylindrical symmetry, the absence of a photon sphere (for neutral strings), or the presence of a stable photon orbit (for charged strings), which strongly affect observable shadows and luminosity patterns. Overall, the study demonstrates how AdS-type geometries imprint distinctive optical signatures, providing a framework to test horizon-scale gravity and discriminate exotic compact objects with future high-resolution VLBI observations, even if AdS cosmology is not observationally favored.

Abstract

The Event Horizon Telescope (EHT) imaging of the central objects in the M87 and Milky Way galaxies provide compelling evidence that these objects are consistent with (Kerr) black holes. In view of these observations and the future expectations of Very Long Baseline Interferometry (VLBI) on which the EHT observations are based, an intensive research work has been carried out in the literature to simulating light trajectories and reconstructing the corresponding optical appearance for a wide array of modified black holes and ultra-compact objects. The corresponding images are directly affected not only by the background space-time geometry but also by the physics of the accretion disk, whose combination yields a characteristic fingerprint. In this paper, we consider such a fingerprint for objects which are not asymptotically flat but instead approach a Anti-de Sitter space-time. This assumption significantly influences light trajectories and, consequently, the corresponding images of the objects as seen by an observer at some distance, which can be used in future VLBI observations for testing alternatives of this kind to the Kerr paradigm. We illustrate our considerations with the examples of a Schwarzschild-Anti-de Sitter black hole and a black string, discussing their most notable departures from canonical, asymptotically-flat black hole space-times.

Figures (17)

• Figure 1: The metric function $A(r)$ for different values of the $M$ parameter for the metric of Schwarzschild-AdS black hole (\ref{['SAdSMetric']}) with $\alpha^2=0.1$.
• Figure 2: The metric function $A(r)$ for different values of $\beta$ for the neutral black string \ref{['ArNeu']} with $\alpha^2=0.1$.
• Figure 3: The metric function $A(r)$ for different values of $\beta$ for the charged black string \ref{['ArChar']} with $\alpha^2=0.1$.
• Figure 4: Number of half- turns $n$ around an asymptotically flat Schwarzschild black hole as a function of the impact parameter $b$.
• Figure 5: Trajectories in the equatorial plane of light rays with $b \in (0,10)$ for the asymptotically flat Schwarzschild black hole. Colours correspond to the direct emission $n=0$ (green) and to the $n=1$ (orange) and $n=2$ (red) photon ring emissions in the observer's plane image. Those curves in gray, purple and light blue also turn $n=0,1,2$, respectively, but from the event horizon towards the asymptotic observer, therefore belonging to the shadow in the observer's image.