Reduced Total Energy Requirements for the Natario Warp Drive Spacetime using Heaviside Step Functions as Analytical Shape Functions

Abstract : 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(the right side of the Einstein Field Equations) for the Einstein tensor $G_{00}$ 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 are the huge negative energy density requirements to sustain a stable warp bubble configuration. Ford and Pfenning computed these negative energy and concluded that at least $10$ times the mass of the Universe is required to sustain a warp bubble configuration. However both Alcubierre and Natario warp drives as members of the same family of the Einstein Field Equations requires the so-called shape functions in order to be mathematically defined. We present in this work two new shape functions for the Natario warp drive spacetime based on the Heaviside step function and one of these functions allows arbitrary superluminal speeds while keeping the negative energy density at "low" and "affordable" levels.We do not violate any known law of quantum physics and we maintain the original geometry of the Natario warp drive spacetime We also discuss briefly Horizons and infinite Doppler blueshifts.
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2012
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Fernando Loup, Rocha Daniel. Reduced Total Energy Requirements for the Natario Warp Drive Spacetime using Heaviside Step Functions as Analytical Shape Functions. 2012. 〈hal-00760456〉

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