Influence of anisotropic matter on the Alcubierre metric and other related metrics: revisiting the problem of negative energy

TL;DR

This paper demonstrates that negative energy densities in warp metrics like Alcubierre's are not necessarily required when considering anisotropic matter and solving the full Einstein equations, challenging previous assumptions.

Contribution

It shows that negative energy densities are not intrinsic to warp metrics when anisotropic fluids are included and the Einstein equations are fully analyzed.

Findings

Negative energy densities are not mandatory in warp metrics.

Anisotropic matter can satisfy Einstein equations without negative energy.

Cylindrical and spherical coordinates facilitate systematic analysis of warp metrics.

Abstract

Negative energy scenarios are the most widely studied for the warp metric. In fact, the prevailing view in the community so far has been that the warp metric necessarily has negative energies. In this work it is shown that the issue of negative energy densities associated with the Alcubierre warp metric with a general form function and similar metrics can be addressed when the whole non--vacuum Einstein equations of the system are examined. To this end, we have considered matter content in the form of anisotropic fluids. We have succeeded in writing the Einstein equations in such a way that some general constraints on the material content become evident. This means that, in rectangular coordinates, the energy density depends necessarily on the tangential pressures of the fluid. For matter such as dust or isotropic fluids we find that density and other related quantities become identically zero. This makes the negative energy problem spurious. It is also revealed that constructing Alcubierre-based metrics using cylindrical and spherical coordinates results in a system of equations that are amenable to more systematic analysis. The field equations constrain the dependence of the form function and how this impacts the matter content. In all cases we determine that energy density is not mandatory negative, despite the recurrent claims in the literature.This result prompts a reevaluation of the negative energy requirements and underscore the importance of cylindrical and spherical type-warps to demonstrate that negative energy density is not an intrinsic unavoidable feature of warp drives.