# Can an underdensity in space act as a negative matter density powering a warp drive?

Consider a homogeneous isotropic universe filled with a perfect fluid with density $$\rho$$ and pressure $$P = \rho/w$$. E.g. for $$w=-1$$ we get a universe equivalent to one with "vacuum energy" or with the cosmological constant.

However, consider now that it is really a perfect fluid with which we can manipulate and $$w$$ is more or less arbitrary. Considering General relativity, could a relative underdensity of the fluid in the shape of a ring act as exotic matter powering a warp drive of an Alcubierre type?

Note that I want to ask only about the formal solution of Einstein equations and whether a similar metric to the one proposed by Alcubierre can be achieved without negative matter density.

This question is one of the questions breaking up the discussion of this question into smaller pieces.

• A downvote? Care to explain?
– Void
Commented Jul 31, 2014 at 16:46

The cosmological constant may perhaps be considered an example of a "perfect fluid" because $p,\rho$ fully specify its state. But they actually overdetermine it. For an environment to be called the cosmological constant, $w=p/\rho$ has to be equal to $-1$ so the value of $w$ surely cannot be "manipulated". Otherwise the stress-energy tensor isn't proportional to the metric tensor – otherwise the "medium" isn't cosmological constant.
Also, the value of $p$ and $\rho$ – and we always have $p=-\rho$, I repeat – is constant in time and space. That's why this concept introduced by Einstein was called the cosmological constant. The very word "constant" means that its values cannot be modified in any way.
There exist genuine or hypothetical materials with $-1\leq w \leq +1$, with the vicinity of $w=+1$ being controversial ("the black hole gas"). For example, the cosmic domain walls and cosmic strings would have $w=-2/3$ and $w=-1/3$, respectively. Radiation has $w=+1/3$ while the dust has $w=0$, of course. However, one can't achieve $|w|\gt 1$ which would violate the null energy condition. The speed of sound in that environment would have to be greater than the speed of light which is not allowed by relativity.