[Paper Review] Image of the thin accretion disk around compact objects in the Einstein-Gauss-Bonnet gravity

Galin Gyulchev, Petya Nedkova+2 more|arXiv (Cornell University)|Jun 28, 2021

Astrophysical Phenomena and Observations44 references59 citations

TL;DR

This paper investigates the optical appearance of thin accretion disks around compact objects in four-dimensional Einstein-Gauss-Bonnet gravity, focusing on black holes and naked singularities. While Gauss-Bonnet black holes resemble Schwarzschild black holes in their images, naked singularities exhibit a distinctive feature: multiple bright concentric rings in the central region due to a stable light ring and repulsive gravitational field near the singularity. These rings emit up to 1,000 times more flux than the primary disk, offering a strong observational signature of modified gravity beyond general relativity.

ABSTRACT

We study the optical appearance of a thin accretion disk around compact objects within the Einstein-Gauss-Bonnet gravity. Considering static spherically symmetric black holes and naked singularities we search for characteristic signatures which can arise in the observable images due to the modification of general relativity. While the images of the Gauss-Bonnet black holes closely resemble the Schwarzschild black hole, naked singularities possess a distinctive feature. A series of bright rings are formed in the central part of the images with observable radiation $10^3$ times larger than the rest of the flux making them observationally significant. We elucidate the physical mechanism, which causes the appearance of the central rings, showing that the image is determined by the light ring structure of the spacetime. In a certain region of the parametric space the Gauss-Bonnet naked singularities possess a stable and an unstable light ring. In addition the gravitational field becomes repulsive in a certain neighbourhood of the singularity. This combination of features leads to the formation of the central rings implying that the effect is not specific for the Einstein-Gauss-Bonnet gravity but would also appear for any other compact object with the same characteristics of the photon dynamics.

Motivation & Objective

• To investigate the observable optical signatures of thin accretion disks in four-dimensional Einstein-Gauss-Bonnet gravity.
• To compare the images of Gauss-Bonnet black holes and naked singularities with those in general relativity, particularly the Schwarzschild solution.
• To identify and characterize unique observational features of naked singularities arising from modified photon dynamics.
• To determine whether the formation of multiple bright rings is a generic feature of spacetimes with stable light rings and repulsive gravity near singularities.

Proposed method

• The study uses exact static, spherically symmetric solutions of 4D Einstein-Gauss-Bonnet gravity with a metric function f(r) dependent on mass M and coupling constant γ.
• Photon trajectories are modeled using null geodesics governed by an effective potential V_eff^ph = L²f(r)/r², with turning points and impact parameters analyzed to identify photon spheres and light rings.
• The images of accretion disks are computed via ray-tracing from a distant observer at large radius and high inclination (i = 80°), tracking multiple orders of images (k = 0 to k = 9).
• The analysis distinguishes between direct images (k=0) and higher-order secondary images formed by photons that orbit the compact object multiple times before reaching the observer.
• The physical mechanism behind image formation is linked to the presence of both a stable light ring and a repulsive gravitational field region near the singularity in weakly naked singularities.
• The flux distribution and image morphology are compared across different values of the dimensionless coupling constant ˆγ = γ/M², focusing on ˆγ ∈ (1, 3√3/4) for naked singularities.

Experimental results

Research questions

• RQ1 How do the images of thin accretion disks in Einstein-Gauss-Bonnet gravity differ from those in general relativity for black holes?
• RQ2 What physical mechanisms in naked singularities of Gauss-Bonnet gravity lead to the formation of multiple bright rings in the central region of the disk image?
• RQ3 Why do some images of the accretion disk in Gauss-Bonnet naked singularities emit up to 1,000 times more flux than the primary image?
• RQ4 Can the presence of a stable light ring and repulsive gravity near the singularity explain the formation of multiple high-order images?
• RQ5 Is the observed ring-like image structure a generic feature of any compact object with similar photon dynamics, regardless of the underlying gravity theory?

Key findings

• Gauss-Bonnet black holes produce accretion disk images that are visually indistinguishable from Schwarzschild black holes, with only minor quantitative differences in disk size and peak flux.
• Naked singularities with 1 < ˆγ < 3√3/4 exhibit a unique feature: a series of concentric bright rings in the central region of the primary disk image, formed by multiple high-order images of the accretion disk.
• The flux from the brightest of these central rings is up to 1,000 times greater than the flux from the primary disk image, making them highly observable.
• The formation of these rings is caused by the coexistence of a stable light ring and a region of repulsive gravity near the singularity, which allows photons to scatter multiple times before escaping to infinity.
• The mechanism is rooted in the effective potential for null geodesics, where photons with impact parameters below the photon sphere can undergo multiple turns around the stable light ring before reaching a distant observer.
• The phenomenon is not specific to Einstein-Gauss-Bonnet gravity but would occur in any spacetime with a stable light ring and repulsive gravity near the singularity, suggesting a generic observational signature for such compact objects.