  The Birkhoff theorem is a well-known result in general relativity and it is
used in many applications. However, its most general version, due to Bona, is
almost unknown and presented in a form less accessible to the relativist and
cosmologist community. Moreover, many wield it mistakenly as a simple
transposition of Newton's iron sphere theorem. In the present work, we propose
a modern, dual null, presentation --- useful in many explorations, including
black holes --- of the theorem that renders accessible most of the results of
Bona's version. In addition, we discuss the fluid contents admissible for the
application of the theorem, beyond a vacuum, and we demonstrate how the
formalism greatly simplifies solving the dynamical equations and allows one to
express the solution as a power expansion in $r$. We present a family of
solutions that share the properties predicted by the Birkhoff theorem and
discuss the existence of trapped and antitrapped regions. The formalism
manifestly shows how the type of region --- trapped or untrapped --- determines
the character of the Killing vector.
