Linearized gravity in isotropic coordinates in the brane world - art. no. 065015

We solve the Einstein equations in the Randall-Sundrum framework using an i sotropic ansatz for the metric and obtain an exact expression to first orde r in the gravitational coupling. The solution is free from metric singulari ties 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 physica l brane this solution coincides with the 4D Schwarzschild metric in isotrop ic coordinates. Furthermore, we show that the extension of the standard Sch warzschild horizon in the bulk is tubular for any diagonal form of the metr ic while there is no restriction for the extension of the Schwarzschild hor izon in isotropic coordinates.