Novel Realizations of Warp Drive Spacetimes as Solutions of General Relativity

TL;DR

This paper critically examines warp drive solutions in general relativity, analyzing their kinematics, stability, and potential for physical realization, and introduces a framework linking warp fields to relativistic cosmology.

Contribution

It provides new insights into warp drive metrics, analyzes their stability, and proposes a relativistic perturbation framework connecting warp fields with cosmological models.

Findings

Identified limitations in Alcubierre's warp drive model.

Found generic instability in certain warp field solutions.

Proposed a relativistic Lagrangian perturbation approach for warp fields.

Abstract

We first take a closer look at the original warp drive proposal by Alcubierre, examine its kinematics in the context of a covariant 3+1 setting, and explain some drawbacks of this construction. In this model, changes of the velocity profile are suppressed, apart from an externally given amplitude. We then discuss Einstein's equations for currently employed spacetime restrictions, and provide the governing equations for the Nat\'ario class of metrics with one-component coordinate velocity in a subcase. Following Synge's G-method we determine the constraints on realizations for two examples: assuming the form of the solution a priori as in Alcubierre's model, and determining the solution through an assumption imposed along geodesics. We analyze in detail the role of coordinate acceleration and coordinate vorticity, providing illustrations for both example solutions. For the second we find an expected generic instability of the warp field. We then propose a framework that allows for spatial curvature and the description of warp field dynamics within a relativistic Lagrangian perturbation approach, also including exact solutions of the Szekeres class II. These generalizations allow us to link studies on warp fields to relativistic cosmology. A direct correspondence between solutions of Newtonian gravity and general relativity is exploited. We conclude by discussing possible future paths towards physical warp drives within tilted fluid flows.