General relativity explains gravity as the curvature of
spacetime. It's all about geometry. The basic equation
of general relativity is called Einstein's equation. In units
, it says
This is a pity, because in fact there is an easy way to express the whole content of Einstein's equation in plain English. In fact, after a suitable prelude, one can summarize it in a single sentence! One needs a lot of mathematics to derive all the consequences of this sentence, but it is still worth seeing -- and we can work out some of its consequences quite easily.
In what follows, we start by outlining some differences between special and general relativity. Next we give a verbal formulation of Einstein's equation. Then we derive a few of its consequences concerning tidal forces, gravitational waves, gravitational collapse, and the big bang cosmology. In the last section we explain why our verbal formulation is equivalent to the usual one in terms of tensors. This article is mainly aimed at those who teach relativity, but except for the last section, we have tried to make it accessible to students, as a sketch of how the subject might be introduced. We conclude with a bibliography of sources to help teach the subject.
© 2006 John Baez and Emory Bunn