[Paper Review] Light ring images of double photon spheres in black hole and wormhole spacetimes

Merce Guerrero, Gonzalo J. Olmo+2 more|arXiv (Cornell University)|Apr 26, 2022

Astrophysical Phenomena and ObservationsPhysics and Astronomy67 references72 citations

TL;DR

This paper investigates light ring images in spherically symmetric black hole and wormhole spacetimes with double photon spheres, using a uniparametric family of extended Schwarzschild metrics. By modeling geometrically thin accretion disks, it demonstrates that two critical curves produce additional concentric light rings between them, offering a clear observational discriminator for black hole mimickers beyond Kerr black holes.

ABSTRACT

The silhouette of a black hole having a critical curve (an unstable bound photon orbit) when illuminated by an optically thin accretion disk whose emission is confined to the equatorial plane shows a distinctive central brightness depression (the shadow) whose outer edge consists of a series of strongly lensed, selfsimilar rings superimposed with the disk???s direct emission. While the size and shape of the critical curve depend only on the background geometry, the pattern of bright and dark regions (including the size and depth of the shadow itself) in the image is strongly influenced by the (astro)physics of the accretion disk. This aspect makes it difficult to extract clean and clear observational discriminators between the Kerr black hole and other compact objects. In the presence of a second critical curve, however, observational differences become apparent. In this work we shall consider some spherically symmetric black hole and wormhole geometries characterized by the presence of a second critical curve, via a uniparametric family of extensions of the Schwarzschild metric. By assuming three toy models of geometrically thin accretion disks, we show the presence of additional light rings in the intermediate region between the two critical curves. The observation of such rings could represent a compelling evidence for the existence of black hole mimickers having multiple critical curves.

Motivation & Objective

• To identify observational signatures that distinguish Kerr black holes from alternative compact objects with multiple critical curves.
• To analyze how the presence of two unstable photon orbits (critical curves) alters the optical appearance of compact objects with accretion disks.
• To explore whether double photon spheres in modified gravity or wormhole geometries produce distinct, observable light ring patterns.
• To assess the detectability of these features using geometrically thin accretion disk models under spherically symmetric spacetimes.
• To provide a theory-agnostic framework for testing deviations from Kerr black hole predictions via lensed ring structures.

Proposed method

• Uses a uniparametric family of extended Schwarzschild metrics that interpolate between black holes and traversable wormholes, allowing for two critical curves.
• Applies null geodesic equations to trace photon trajectories in these spacetimes, identifying unstable circular orbits (critical curves) via the effective potential analysis.
• Models three toy accretion disk configurations—optically and geometrically thin—assuming emission confined to the equatorial plane.
• Computes the lensing pattern by integrating photon trajectories from the disk to the observer, identifying self-similar, concentric light rings between the two critical curves.
• Employs numerical ray-tracing techniques within Mathematica® to generate synthetic images of the optical appearance, including the shadow and lensed rings.
• Analyzes luminosity contributions from direct emission and multiple lensed images, emphasizing the exponential suppression of higher-order rings.

Experimental results

Research questions

• RQ1 Can the presence of two critical curves in spherically symmetric spacetimes produce observable, distinct light ring structures not found in Kerr black holes?
• RQ2 How do the positions, sizes, and luminosities of additional light rings depend on the spacetime parameters and the location of the inner disk edge?
• RQ3 To what extent can the pattern of concentric light rings serve as a clean observational discriminator between Kerr black holes and alternative compact objects?
• RQ4 How does the accretion disk's geometry and emission profile affect the visibility and detectability of secondary light rings between two photon spheres?
• RQ5 Are there parameter regimes in the extended Schwarzschild family where the double-ring signature becomes observationally resolvable with current or near-future instruments?

Key findings

• The presence of two critical curves—resulting from a uniparametric extension of the Schwarzschild metric—leads to the formation of additional, concentric light rings in the intermediate region between them.
• These secondary light rings are self-similar and exponentially suppressed in luminosity, similar to the primary ring in Kerr black holes, but appear as distinct features due to the dual critical curve structure.
• The optical appearance is dominated by direct emission and the primary ring near the outer critical curve, but the secondary ring structure emerges clearly in the luminosity profile between the two curves.
• The size and shape of the shadow remain influenced by the background geometry, but the intermediate ring pattern provides a unique, geometry-driven signature independent of accretion disk physics.
• The model predicts that such double-ring patterns could serve as a compelling observational evidence for black hole mimickers such as traversable wormholes or non-Kerr compact objects.
• Numerical simulations confirm that the light ring pattern is robust across different thin disk models, indicating a generic feature of spacetimes with multiple unstable photon orbits.