Modification in Alcubierre Warp Drive Geometry to Preserve Positive Energy Density

Alcubierre introduced the warp drive model in 1994. However, Alcubierre warp drive model resulted in negative energy density everywhere. The purpose of this paper is to show that with a small modification in the Alcubierre warp drive geometry, while keeping the warp drive bubble shape unchanged, we achieved a total positive energy density.