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 starting from $2012$ to $2014$ a set of works appeared in the current scientific literature covering the Natario warp drive with an equation intended to be the original Natario equation however this equation do not obeys the original $3+1$ Arnowitt-Dresner-Misner($ADM$) formalism and hence this equation cannot be regarded as the original Natario warp drive equation.However this new equation satisfies the Natario criteria for a warp drive spacetime and as a matter of fact this equation must be analyzed under a new and parallel contravariant $3+1$ $ADM$ formalism.In this work we introduce also a second new Natario equation but using a parallel covariant $3+1$ $ADM$ formalism. We compare both the original and parallel $3+1$ $ADM$ formalisms wether in contravariant or covariant form using the approach of Misner-Thorne-Wheeler($MTW$) and Alcubierre and while in the $3+1$ spacetime the parallel equations differs radically from the original one when we reduce the equations to a $1+1$ spacetime all the equations becomes equivalent.We discuss the possibilities in General Relativity for these new equations.