Relativity and Cosmology


Reduced Total Energy Requirements For The Original Alcubierre and Natario Warp Drive Spacetimes-The Role Of Warp Factors.

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 G00 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 1028 times the positive energy density of Earth!!!(We multiply the mass of Earth by c2 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.

Download: PDF

Submission history

[v1] 22 Mar 2011
[v2] 5 Apr 2011
[v3] 12 Apr 2011
[v4] 25 Apr 2011

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