Violations of the Weak Energy Condition for Lentz Warp Drives

TL;DR

This paper critically examines Lentz's proposed warp drive spacetime, demonstrating that it violates the Weak Energy Condition despite claims of non-negative energy density, and clarifies the errors in the original derivation.

Contribution

The paper provides a direct calculation of Lentz's warp drive energy-momentum tensor, correcting derivation errors and showing the spacetime still violates the Weak Energy Condition.

Findings

Lentz's warp drive has regions with negative energy density.

Corrected derivation still violates the Weak Energy Condition.

Lentz's claim of non-negative energy density is incorrect.

Abstract

Warp drive spacetimes capable of superluminal transportation, were first introduced in 1994 by Miguel Alcubierre and then generalized by others. These spacetimes violated the Weak Energy Condition (WEC). Lentz proposed a new type of warp drive in 2020. It was claimed that this warp spacetime has non-negative energy density and can therefore be sourced by a classical plasma. We demonstrate that Lentz's claim is incorrect. We begin with a direct calculation of the energy-momentum tensor of Lentz's warp drive in a Eulerian reference frame, and show that there are spacetime regions where the energy density is negative. We then examine the theoretical basis of Lentz's investigation and identify several derivation errors. The derivation errors can be somewhat ameliorated with a modified version of Lentz's geometry, which more closely respects the equalities and inequalities discussed by Lentz. Even so, we show that the modified geometry still violates the WEC even in the Eulerian reference frame. We conclude with a brief discussion of no-go theorems and their relationship to geometries of the kind proposed by Lentz.