Birkhoff's theorem in the f(T) gravity
  Generalized from the so-called teleparallel gravity which is exactly
equivalent to general relativity, the $f(T)$ gravity has been proposed as an
alternative gravity model to account for the dark energy phenomena. In this
letter we prove that the external vacuum gravitational field for a spherically
symmetric distribution of source matter in the $f(T)$ gravity framework must be
static and the conclusion is independent of the radial distribution and
spherically symmetric motion of the source matter that is, whether it is in
motion or static. As a consequence, the Birkhoff's theorem is valid in the
general $f(T)$ theory. We also discuss its application in the de Sitter
space-time evolution phase as preferred to by the nowadays dark energy
observations.
