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The basic concepts

In the theory of general relativity, gravity is treated as a curvature of space-time instead of a force. A point in the 4-dimensional space-time is called an event. The trajectory of a body in space-time is called a world line.

The separation ds between to infinitely close events with coordinates tex2html_wrap_inline808 and tex2html_wrap_inline810 , respectively, is given by


where tex2html_wrap_inline812 is the metric tensor. We use the Einstein summation convention: repeated indices are to be summed over. If we wrote the above equation with explicit summation, it would be


We can chose any coordinates we like. For black holes, which a spherical symmetrical, time + spherical polar coordinates, tex2html_wrap_inline1194 , are well suited.

Web Exhibition: Null Geodesics Around a Kerr Black Hole

Bo Milvang-Jensen (
Mon Jun 17 11:54:08 MDT 1996