The Analysis of Barcelo,Finazzi and Liberati applied to both Alcubierre and Natario Warp Drive Spacetimes: Horizons,Infinite Doppler Blueshifts and Quantum Instabilities(Natario <> Alcubierre)

Fernando Loup (1)

1 REU - Residencia De Estudantes Universitas

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 is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive is the huge amount of negative energy able to sustain the warp bubble.In order to perform an interstellar space travel to a "nearby" star at $20$ light-years away with $3$ potential habitable exo-planets(Gliese $667c$) at superluminal speeds 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!!! Some years ago Barcelo,Finazzi and Liberati published a work in which the composed mixed tensor $\langle {T_\mu}^\nu\rangle$ obtained from the negative energy density tensor $T_{\mu\nu}$ $\mu=0,\nu=0$ of the $1+1$ dimensional Alcubierre warp drive metric diverges when the velocity of the ship $vs$ exceeds the speed of light.(see pg $2$ in \cite{ref19}).We demonstrate in this work that in fact this do not happens and their results must be re-examined.We introduce here a shape function that defines the Natario warp drive spacetime as an excellent candidate to low the negative energy density requirements from $10^{48}$ to affordable levels.We also discuss Horizons and Doppler Blueshifts that affects the Alcubierre spacetime but not the Natario counterpart.

Mots clés: Alcubierre; Natario; Warp Drive; Superluminal Phtysics; Negative Energy

Domaines: Physique mathématique [math-ph]

Fernando Loup. The Analysis of Barcelo,Finazzi and Liberati applied to both Alcubierre and Natario Warp Drive Spacetimes: Horizons,Infinite Doppler Blueshifts and Quantum Instabilities(Natario <> Alcubierre). 2013. ⟨hal-00879381⟩