  We solve the Einstein equations in the Randall-Sundrum framework using an
isotropic ansatz for the metric and obtain an exact expression to first order
in the gravitational coupling. The solution is free from metric singularities
away from the source and it satisfies the Israel matching condition on a
straight brane. At distances far away from the source and on the physical brane
this solution coincides with the 4-D Schwarzschild metric in isotropic
coordinates. Furthermore we show that the extension of the standard
Schwarzschild horizon in the bulk is tubular for any diagonal form of the
metric while there is no restriction for the extension of the Schwarzschild
horizon in isotropic coordinates.
