Perfect fluid warp drive solutions with the cosmological constant

TL;DR

This paper explores solutions to Einstein's equations with a cosmological constant for the Alcubierre warp drive, revealing complex energy-matter configurations needed for superluminal travel and questioning the necessity of negative matter.

Contribution

It extends warp drive solutions to include the cosmological constant and perfect fluids, analyzing energy conditions and the complexity of matter required for superluminal speeds.

Findings

Off-diagonal energy-momentum components are necessary for warp bubble motion.

Superluminal speeds may not require negative matter.

More complex matter distributions are needed for stable warp drive solutions.

Abstract

The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities. In this work we advance solutions of the Einstein equations with the cosmological constant for the Alcubierre warp drive metric having the perfect fluid as source. We also consider the particular dust case with the cosmological constant, which generalizes our previous dust solution (arXiv:2008.06560) and led to vacuum solutions connecting the warp drive with shock waves via the Burgers equation, as well as our perfect fluid solution without the cosmological constant (arXiv:2101.11467). All energy conditions are also analyzed. The results show that the shift vector in the direction of the warp bubble motion creates a coupling in the Einstein equations that requires off-diagonal terms in the energy-momentum source. Therefore, it seems that to achieve superluminal speeds by means of the Alcubierre warp drive spacetime geometry one may require a complex configuration and distribution of energy, matter and momentum as source in order to produce a warp drive bubble. In addition, warp speeds seem to require more complex forms of matter than dust for stable solutions and that negative matter may not be a strict requirement to achieve global superluminal speeds.