  We investigate possible configurations for vacuum multi-black holes that
maintain static equilibrium in expanding bubbles. Our analysis assumes a
five-dimensional Weyl metric to describe the spacetime, facilitating the
derivation of solutions based on the provided rod structure. We consider a
spacetime having expanding bubbles caused by one or two acceleration horizons,
and show that various configurations such as two bubbles, four bubbles devoid
of horizons, a black saturn, a black di-ring, a bicycling black ring
(orthogonal black di-ring), and a five-dimensional black hole binary can
achieve equilibrium within expanding bubbles. Specifically, we demonstrate that
equilibrium requires two acceleration horizons on both sides for the bicycling
ring and the five-dimensional black hole binary. However, only one acceleration
horizon is necessary for achieving equilibrium in the case of the black saturn
and the black di-ring.
