Relativity and Cosmology

   

An Extended Version of the Natario Warp Drive Equation Based in the Original $3+1$ $adm$ Formalism Which Encompasses Accelerations and Variable Velocities

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 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.However both the Alcubierre or Natario warp drive spacetimes always have a constant speed in the internal structure of their equations which means to say that these warp drives always travel with a constant speed.But a real warp drive must accelerate from zero to a superluminal speed of about $200$ times faster than light in the beginning of an interstellar journey and de-accelerate again to zero in the end of the journey.In this work we expand the Natario vector introducing the coordinate time as a new Canonical Basis for the Hodge star and we introduce an extended Natario warp drive equation which encompasses accelerations.

Comments: 46 Pages. develops a Natario warp drive which encompasses accelerations

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[v1] 2017-12-07 08:00:34

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