[Paper Review] Shadow of rotating black holes on a standard background screen

S. Repin, Dmitry A. Kompaneets+2 more|arXiv (Cornell University)|Feb 12, 2018

Astrophysical Phenomena and Observations9 references3 citations

TL;DR

This paper investigates the gravitational lensing effects of rotating black holes on a distant, uniformly emitting standard screen, simulating the shadow observed by a distant observer. By tracing null geodesics from the observer to the screen using Kerr and Schwarzschild metrics, it reveals that the shadow's shape and intensity distribution depend critically on the angle between the screen's normal and the line of sight, with strong lensing producing bright, distinct internal arcs near the shadow edge, especially in optically thin conditions.

ABSTRACT

We present the shape of the black hole shadow on the standard background screen as it is registered by the distant observer. The screen is an infinite plane, emitting the quanta uniformly distributed to a hemisphere. The source of emission is considered to be optically thin and optically thick. It is shown that the shape of a black hole shadow depends crucially on the angle between the plane and the view line to the distant observer. The shadow shapes for the different values of this angle are also presented. Both Schwarzschild and Kerr metrics are considered.

Motivation & Objective

• To isolate and analyze the pure gravitational lensing effects of black holes on a simple, uniform background screen, independent of complex astrophysical structures like accretion disks.
• To determine how the observed shadow shape and intensity distribution vary with the inclination angle between the observer’s line of sight and the normal to the background screen.
• To compare the effects of optically thin and optically thick emission from the background screen on the resulting shadow morphology.
• To provide a baseline model for interpreting real observations of black hole shadows, such as those from the Event Horizon Telescope, by disentangling lensing signatures from astrophysical emission complexity.

Proposed method

• Simulates photon trajectories from a distant observer back to a uniformly emitting, infinite plane (standard screen) located at 1000 r₉ from the black hole.
• Uses numerical integration of null geodesics in Kerr and Schwarzschild spacetimes to trace light paths from observer to screen, avoiding computationally wasteful forward tracing.
• Considers the screen at fixed distance (1000 r₉) but varies its orientation relative to the observer’s line of sight, introducing angles from −80° to +80°.
• Computes the intensity distribution on the observer’s sky by mapping screen emission to the lensed image, distinguishing between optically thin and thick emission models.
• Applies a coordinate transformation to avoid infinite distances in the simulation, placing the observer and screen at finite, symmetric positions relative to the black hole.
• Visualizes the shadow and intensity distribution using color-mapped images with grid resolution of 2 r₉, focusing on the edge and internal ring structures.

Experimental results

Research questions

• RQ1 How does the inclination angle between the observer’s line of sight and the normal to the background screen affect the shape and structure of the black hole shadow?
• RQ2 What are the observable features in the intensity distribution around the black hole shadow, particularly near the edge and in internal ring-like structures?
• RQ3 How do the optical thickness properties of the background screen (thin vs. thick) influence the observed intensity profile near the shadow boundary?
• RQ4 To what extent do the lensing effects of rotating black holes (Kerr metric) modify the apparent size and distortion of the shadow compared to non-rotating black holes (Schwarzschild metric)?
• RQ5 Can distinct, lensing-induced features such as bright internal arcs be reliably identified in the shadow image, independent of accretion disk physics?

Key findings

• The shadow shape and intensity distribution are highly sensitive to the angle between the observer’s line of sight and the normal to the background screen, with significant asymmetries appearing at oblique angles.
• For optically thin screens, the intensity near the shadow edge diverges to infinity, and distinct, bright internal arcs form, especially visible in the equatorial plane at 45° and 60° inclinations.
• When the screen is on the opposite side of the observer (negative angles), the inner annulus becomes bolder and brighter, with resolvable sub-structures such as fine rings visible near the edge.
• The intensity difference between optically thin and thick screens is negligible except very close to the shadow boundary, indicating that far regions of the screen dominate the observed brightness.
• The internal ring structures, which can span 3–4 microarcseconds in nearby galaxies like M87 and M31, are robust lensing features that could be detectable with high-resolution interferometers.
• The results demonstrate that pure gravitational lensing produces complex, observable features in the shadow image—such as bright, ring-like structures—providing a clean signature of black hole spacetime geometry independent of accretion physics.