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We solve the Einstein equations in the Randall-Sundrum framework using anisotropic ansatz for the metric and obtain an exact expression to first orderin the gravitational coupling. The solution is free from metric singularitiesaway from the source and it satisfies the Israel matching condition on astraight brane. At distances far away from the source and on the physical branethis solution coincides with the 4-D Schwarzschild metric in isotropiccoordinates. Furthermore we show that the extension of the standardSchwarzschild horizon in the bulk is tubular for any diagonal form of themetric while there is no restriction for the extension of the Schwarzschildhorizon in isotropic coordinates.Comment: 13 pages, plain Te

Linearized gravity in isotropic coordinates in the brane world