  Motivated by the newest progress in geometric flows both in mathematics and
physics, we apply the geometric evolution equation to study some black-hole
problems. Our results show that, under certain conditions, the geometric
evolution equations satisfy the Birkhoff theorem, and surprisingly, in the case
of spherically symmetric metric field, the Einstein equation, the Ricci flow,
and the hyperbolic geometric flow in vacuum spacetime have the same black-hole
solutions, especially in the case of $\Lambda=0$, they all have the
Schwarzschild solution. In addition, these results can be generalized to a kind
of more general geometric flow.
