I recently met Rob Hocking, a Canadian mathematician who is passionate about visualizing theoretical physics in photography. He showed me some fascinating images of how everyday objects would appear if a black hole were in the vicinity—a predicament one would think twice about wanting to experience in real life. Those images had been computed using conventional photographs as raw data. ‘Light rays from the object are bent by the black hole en route to the observer, resulting in a distorted appearance which can be artistically pleasing’, says Rob. The bending effect is called gravitational lensing, a term photographers may find appealing.
In the figure above, light rays from different directions are deflected to varying extents by a black hole before reaching the observer’s eye, including rays (example in blue) from behind, making it possible to see objects not normally within the human field of vision. In order to accommodate this, a photograph that sees in all directions must be used to generate the hypothetical image of ‘environmental’ black holes. This photograph, known as a spherical panorama, is a composite of photographs covering all points on a sphere with the camera in its centre. The number of photographs needed to construct the panorama depends on the focal length of the camera lens and the desired resolution.
This is a spherical panorama of Rob and his yoga instructor Kevin Elander, which stretches the floor and ceiling in the same way that Antarctica and the Arctic are projected on many world maps. The panoramic tripod head that Rob uses can be seen in the mirror at far left. It has been programmed to rotate the camera through 40 different positions while keeping the optical centre fixed. The only direction it cannot look is straight down; that view is covered by an additional, handheld photograph.
There is an ingenious device, patent pending at press time, for capturing spherical panoramas. This consists of a ball studded with cameras pointing in all directions. The ball is thrown into the air. When it reaches maximum altitude, the internal motion sensor sets off all the cameras at once. I assume it survives the impact of return to earth.
Given the panoramic photograph, the next step is to calculate the trajectories of the deflected photons using the geodesic equations from Einstein’s general theory of relativity. This information is then used to remap the photographic pixels. The following diagram shows four calculated examples of the infinitely many possible trajectories of photons around a black hole on their way from a given point to the observer. Photons may orbit the black hole any number of times before shooting off at a tangent.
The remapping of the yoga photograph is shown below, with two black holes situated above the yoga and math gurus. Because of the infinite number of photon paths, there are in fact infinitely many secondary images of the gurus around each black hole if we assume infinite photographic resolution; only one of the images is visible for each black hole, the rest being too small to be resolved on the digital display. This example is intriguing as it incorporates two interacting black holes.
Here is another of Rob’s spherical panoramas featuring the Great Wall of China, along with one of his signature black hole photos derived from it. The odd patch in the sky is not a renegade black hole—it is the consequence of camera misalignments during the production of the composite photographs. Rob had to handhold the camera, not having a panoramic tripod head at his disposal at the time.
Check out more of Rob’s thought-provoking photographs here. I’m grateful to Rob for telling me about his work and for his valuable assistance with the editing of this post.
Rob Hocking is a PhD student at the Faculty of Mathematics, University of Cambridge. It’s great to meet someone who is able to unify the photographic and relativistic meanings of the slogan where Photons meet Black Holes. See more of Rob’s fascinating stuff at his blog.