Black Hole Vision: An Interactive iOS Application for Visualizing Black Holes

TL;DR

How light rays are lensed by non-rotating (Schwarzschild) and rotating (Kerr) black holes are described, and the equations needed for computing black-hole-lensed images are listed.

Abstract

The Black Hole Explorer (BHEX) is a proposed mission to launch a sub-millimeter radio telescope into Earth orbit that will take the sharpest images in the history of astronomy and reveal novel horizon-scale features of supermassive black holes. Black Hole Vision is an open-source application, freely available on the iOS App Store, that produces lensed images which highlight the key features expected to appear in the black hole images BHEX will capture. The app combines video feeds from the front- and rear-facing iPhone cameras and uses the black hole lensing equations to synthesize an onscreen image displaying the user's surroundings as if they were gravitationally lensed by a black hole within the cameras' field of view. Here, we describe how light rays are lensed by non-rotating (Schwarzschild) and rotating (Kerr) black holes, and we list the equations needed for computing black-hole-lensed images. We also describe their specific implementation within Black Hole Vision.

Figures (2)

• Figure 1: The screen (yellow plane) and Cartesian coordinates $(\alpha,\beta)$ of an observer (green sphere) at large distance from a black hole (black sphere). The observer screen is the plane through the black hole that is perpendicular to the observer's line of sight (dashed, black line). A photon that reaches the observer traveling along a bent light ray (blue arc) produces an image on the screen (red sphere within the yellow plane) at the apparent position of the source in the sky of the observer. This figure originally appeared in Appendix E of Gralla2017.
• Figure 2: In Schwarzschild, for a given choice of polar angle $\psi$ on the screen, coordinates can be chosen such that all photons with apparent position on the ray of constant $\psi$ have trajectories that lie within the equatorial plane---one such trajectory is illustrated here (blue arc). To implement step (3), one needs only one lensing calculation: the computation of $\phi_S(\lambda)$, the azimuthal angle accrued along the photon trajectory from observer (green circle) to source sphere (dashed, circular arc). The intersection point (red circle) is used to determine the color of the corresponding pixel. Also shown is the apparent position (red circle) on the screen (dashed, vertical line) of the photon trajectory under consideration, with its corresponding distance of $\lambda = \sqrt{\alpha^2 + \beta^2}$.