Two Kinds of Black Holes in an Electric Universe

The internal symmetry groups was found by Kinnersley in the Ernst's equation,In this paper we adopted the Harrison's transformation in groups and obtained exact expressions for the exterior metric field associated with Schwarzschild and Reissner-Nordstrom black holes in an electric universe.There is an arbitrary parameter E 0 in the expressions,it expresses a uniform electric field in the direction opposite to the polar axis.We found that the R-N metric form in an electric universe is static, and it is different from the metric form in a magnetic universe.