Relativity and Cosmology

   

The Analysis of Chris Van Den Broeck Applied to the Natario Warp Drive Spacetime Using the Original Alcubierre Shape Function to Generate the Broeck Spacetime Distortion:the Natario-Broeck Warp Drive

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 the major drawback concerning warp drives is the huge amount of negative energy density able to sustain the warp bubble.In order to perform an interstellar space travel to a "nearby" star at $20$ light-years away in a reasonable amount of time a ship must attain a speed of about $200$ times faster than light.However the negative energy density at such a speed is directly proportional to the factor $10^{48}$ which is $1.000.000.000.000.000.000.000.000$ times bigger in magnitude than the mass of the planet Earth!!. With the correct form of the shape function the Natario warp drive can overcome this obstacle at least in theory.Other drawbacks that affects the warp drive geometry are the collisions with hazardous interstellar matter(asteroids,comets,interstellar dust etc)that will unavoidably occurs when a ship travels at superluminal speeds and the problem of the Horizons(causally disconnected portions of spacetime).The geometrical features of the Natario warp drive are the required ones to overcome these obstacles also at least in theory.Some years ago in $1999$ Chris Van Den Broeck appeared with a very interesting idea.Broeck proposed a warp bubble with a large internal radius able to accommodate a ship inside while having a submicroscopic outer radius and a submicroscopic contact external surface in order to better avoid the collisions against the interstellar matter.The Broeck spacetime distortion have the shape of a bottle with $200$ meters of inner diameter able to accommodate a spaceship inside the bottle but the bottleneck possesses a very small outer radius with only $10^{-15}$ meters $100$ billion time smaller than a millimeter therefore reducing the probabilities of collisions against large objects in interstellar space.In this work we apply the Broeck idea to the Natario warp drive spacetime but out bottle have $200$ kilometers of inner size $1000$ times the size of the original Broeck bottle and we use the original Alcubierre shape function to generate our version of the Broeck bottle with very low energy density requirements.The Broeck idea is more than welcome and solves definitively the problem of the collisions against large objects. Any future development for the Natario warp drive must encompass the Broeck bottle and this approach must be named as the Natario-Broeck warp drive.

Comments: 86 Pages. this paper links the Broeck developments for the Alcubierre warp drive to the Natario warp drive

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[v1] 2017-02-08 07:00:12

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