**Abstract** : 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.