Black Holes in an Expanding Universe
  An exact solution representing black holes in an expanding universe is found.
The black holes are maximally charged and the universe is expanding with
arbitrary equation of state. It is an exact solution of the
Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields
coupled to the scalar field. The potential of the scalar field is an
exponential. We find a regular horizon, which depends on one parameter (the
ratio of the energy density of U(1) fields to that of the scalar field). The
horizon is static because of the balance on the horizon between gravitational
attractive force and U(1) repulsive force acting on the scalar field. We also
calculate the black hole temperature.
