Generic warp drives violate the null energy condition

Abstract

Three recent articles have claimed that it is possible to, at least in theory, either set up positive energy warp drives satisfying the weak energy condition (WEC), or at the very least, to minimize the WEC violations. These claims are, at best, incomplete since the arguments as presented only assert but do not prove the existence of one set of timelike observers, the comoving Eulerian observers, who see relatively ``nice'' physics. While these particular observers might arguably see a positive energy density, the WEC requires all timelike observers to see positive energy density. Therefore, one should carefully revisit this issue. A more careful analysis shows that the situation is actually much grimmer than advertised---within the framework adopted by those three papers all physically reasonable warp drives will certainly violate the WEC, and both the strong and dominant energy conditions. Under plausible subsidiary conditions the null energy condition is also violated. While warp drives are certainly interesting examples of speculative physics, the violation of the energy conditions, at least within the framework of standard general relativity, is unavoidable. Even in modified gravity, physically reasonable warp drives will still violate the purely geometrical null convergence condition and the timelike convergence condition which, in turn, will place very strong constraints on any modified-gravity warp drive.