Virtual spacetime: an environment for the visualization of curved spacetimes via geodesic flows

We describe an implementation of a virtual environment for visualizing the geometry of curved spacetime by the display of interactive geodesics. This technique displays the paths of particles under the influence of gravity as described by the general theory of relativity, and is useful in the investigation of solutions to the field equations of that theory. A boom-mounted six degree of freedom head position sensitive stereo CRT system is used for display. A hand position sensitive glove controller is used to control the initial positions and directions of geodesics in spacetime. A multiprocessor graphics workstation is used for computation and rendering. We describe and illustrate with examples several techniques for visualizing the geometry of spacetime using geodesics. Though this work is described exclusively in the context of physical four-dimensional spacetimes, it extends to arbitrary geometries in arbitrary dimensions. While this work is intended for researchers, it is also useful for the teaching of general relativity.