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

**Authors:** Fernando Loup, Daniel Rocha

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.

**Comments:** 26 Pages.

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### Submission history

[v1] 2012-12-03 16:42:35

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