ADM mass in warp drive spacetimes

TL;DR

This paper rigorously analyzes the concept of mass in warp drive spacetimes, demonstrating that such spacetimes violate all classical energy conditions and clarifying misconceptions about the nature of mass and payloads in warp drives.

Contribution

It provides an exact, explicit computation of stress-energy components in warp drive spacetimes, clarifies the role of mass, and confirms violations of all classical energy conditions.

Findings

Warp drive spacetimes violate NEC, WEC, SEC, DEC.

Explicit stress-energy tensor calculations are provided.

Clarifies the distinction between bubble mass and background features.

Abstract

What happens when a warp bubble has mass? This seemingly innocent question forces one to carefully formalize exactly what one means by a warp bubble, exactly what one means by having the warp bubble "move" with respect to the fixed stars, and forces one to more carefully examine the notion of mass in warp-drive spacetimes. This is the goal of the present article. In this process, we will see that often-made throw-away comments regarding "payloads" are even simpler than commonly assumed, while there are two further, distinct yet subtle ways in which a mass can appear in connection with a warp drive space-time: One, that the warp bubble (not its payload) has the mass; two, that the mass is a background feature in front of which the warp drive moves. For simplicity, we consider generic Nat\'ario warp drives with zero-vorticity flow field. The resulting spacetimes are sufficiently simple to allow an exact and fully explicit computation of all of the stress-energy components, and verify that (as expected) the null energy condition (NEC) is violated. Likewise the weak, strong, and dominant energy conditions (WEC, SEC, DEC) are violated. Indeed, this confirms the community's folk wisdom, and recent (fully general, but implicit) results of the present authors which closed previous gaps in the argument. However, folk wisdom should be carefully and critically examined before being believed, and the present examples for general results will greatly aid physical intuition.