Show HN: Physically accurate black hole simulation using your iPhone camera

Hello! We are Dr. Roman Berens, Prof. Alex Lupsasca, and Trevor Gravely (PhD Candidate) and we are physicists working at Vanderbilt University. We are excited to share Black Hole Vision: https://apps.apple.com/us/app/black-hole-vision/id6737292448.

Black Hole Vision simulates the gravitational lensing effects of a black hole and applies these effects to the video feeds from an iPhone's cameras. The application implements the lensing equations derived from general relativity (see https://arxiv.org/abs/1910.12881 if you are interested in the details) to create a physically accurate effect.

The app can either put a black hole in front of the main camera to show your environment as lensed by a black hole, or it can be used in "selfie" mode with the black hole in front of the front-facing camera to show you a lensed version of yourself.

There are several additional options you can select when using the app. The first lensing option you can select is "Static black hole". In this mode, we simulate a non-rotating (Schwarzschild) black hole. There are two submodes that change the simulated field-of-view (FOV): "Realistic FOV" and "Full FOV". The realistic FOV mode takes into account the finite FOV of the iPhone cameras, leading to a multi-lobed dark patch in the center of the screen. This patch includes both the "black hole shadow" (light rays that end up falling into the black hole) and "blind spots" (directions that lie outside the FOV of both the front-and-rear-facing cameras). The full FOV mode acts as if the cameras have an infinite FOV such that they cover all angles. The result is a single, circular black hole shadow at the center of the screen.

Next, you can select the "Kerr black hole" mode, which adds rotation (spin) to the black hole. Additionally, you can augment the rotational speed of the black hole (its spin, labeled "a" and given as a percentage of the maximal spin).

In a nutshell, the app computes a map from texture coordinate to texture coordinate. This map is itself stored as a texture --- to obtain the value of the map on texture coordinates (x,y), one samples the texture at (x,y) and the resulting float4 contains the outputs (x',y') as well as a status code.

When the user selects the "Static black hole" mode, this texture is computed on the GPU and cached. The "Kerr black hole" textures, however, have been precomputed in Mathematica, due to the need for double precision floating point math, which is not natively available in Apple's Metal shading language.

The source code, including the Mathematica notebook, can be found here https://github.com/graveltr/BlackHoleVision.