Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However as stated by both Alcubierre and Natario themselves the warp drive violates all the known energy conditions because the stress energy momentum tensor is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive is the huge amount of negative energy able to sustain the warp bubble.Ford and Pfenning computed the amount of negative energy needed to maintain an Alcubierre warp drive and they arrived at the result of $10$ times the mass of the entire Universe for a stable warp drive configuration rendering the warp drive impossible.We introduce here $3$ new shape functions that defines the Natario warp drive spacetime and we choose one of these functions as an excellent candidate to low the negative energy density requirements to affordable levels.We demonstrate in this work that both Alcubierre and Natario warp drives have two warped regions and not only one.One of these warped regions is associated with geometry and the other is associated with negative energy requirements.We also discuss Horizons and Doppler Blueshifts that affects the Alcubierre spacetime but not the Natario counterpart.
Numerical Integration of the Negative Energy Density in the Natario Warp Drive Spacetime using $3$ different Natario Shape Functions