**Authors:** Fernando Loup

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 theory allows the existence of very small
amounts of it being the Casimir effect a good example as stated by Alcubierre himself. But the stress
energy momentum tensor of both Alcubierre and Natario Warp Drives have the speed of the ship raised
to the square inside its mathematical structure which means to say that as fast the ship goes by then
more and more amounts of negative energy are needed in order to maintain the Warp Drive. Since the
total energy requirements to maintain the Warp Drive are enormous and since quantum theory only
allows small amounts of it,many authors regarded the Warp Drive as unphysical and impossible to be
achieved. We compute the negative energy density requirements for a Warp Bubble with a radius of
100 meters(large enough to contain a ship) moving with a speed of 200 times light speed(fast enough to
reach stars at 20 light-years away in months not in years)and we verify that the negative energy density
requirements are of about 10^{28} times the positive energy density of Earth!!!(We multiply the mass of
Earth by c^{2} and divide by Earth volume for a radius of 6300km). 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 one
for the Alcubierre and another for the NatarioWarp Drive Spacetimes that 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 geometries of both Alcubierre and Natario
Warp Drive Spacetimes.

**Comments:** 21 pages.

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[v1] 22 Mar 2011

[v2] 5 Apr 2011

[v3] 12 Apr 2011

[v4] 25 Apr 2011

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