Black hole visualization and animation

Black hole visualization is a problem of raytracing over curved spacetimes. This paper discusses the physics of light in curved spacetimes, the geometry of black holes, and the appearance of objects as viewed through a relativistic camera (the Penrose-Terrell effect). It then discusses computational issues of how to generate images of black holes with a computer. A method of determining the most efficient series of steps to calculate the value of a mathematical expression is described and used to improve the speed of the program. The details of raytracing over curved spaces not covered by a single chart are described. A method of generating images of several black holes in the same spacetime is discussed. Finally, a series of images generated by these methods is given and interpreted.