Updated by Don Koks 2008.

Original by Philip Gibbs 1996.

When an object approaches the speed of light, its mass increases without limit, and its length contracts towards zero. Thus its density increases without limit. Sometimes people think that this implies it should form a black hole; and yet, they reason, since its mass and volume haven't changed in its rest frame, it should not form a black hole in that frame—and therefore not in any other frame either. So does a black hole form or not?

The answer is that a black hole does not form. The idea that "if enough mass is
squeezed into a sufficiently small space it will form a black hole" is rather vague.
Crudely speaking, we might say that if an amount of mass, *M*, is contained within
a sphere of radius *2GM/c ^{2}* (the Schwarzschild radius), then it must be
a black hole. But this is based on a particular static solution to the Einstein
field equations of general relativity, and ignores momentum and angular momentum as well
as the dynamics of spacetime itself. In general relativity, gravity does not only
couple to mass as it does in the newtonian theory of gravity. Gravity also couples
to momentum and momentum flow; the gravitational field is even coupled to itself. It
is actually quite difficult to determine the correct conditions for a black hole to
form. Hawking and Penrose proved a number of useful singularity theorems about the
formation of black holes. But even these theorems do assume certain conditions which
we cannot be sure are true "out there".