Visualization in Curved Spacetimes

Summary

A possibility for the visualization of arbitrary objects in curved space-times is the computation of an image as a realistic observer would see it. We present this approach first in the context of special relativity. In particular, we discuss the ‘apparent geometry’ of a moving object and the effects on the specific intensity that is seen by the observer. We examine the possibility of using polygon shading as an alternative technique, which is simpler than a full ray-tracing approach. In general relativity, no such shortcut is possible, and we have to explicitly integrate the paths of all photons reaching the observer. The resulting image is therefore determined not only by the object itself, but also by the spacetime surrounding this object. In addition, the observer may now have to be described in a general relativistic context. We also discuss the possibility of including general relativistic ray-tracing in conventional ray-tracing software. As examples, we present pictures of a thin disc around a Kerr black hole and of Einstein rings. We also mention astrophysical consequences of the distortion of images as they occur for light curves of X-ray pulsars or spectra measured for accretion disks around compact objects. Examples for pictures and animations can be found on the World Wide Web, our home page is http://www.tat.physik.uni-tuebingen.de.