Curvature Invariants for Wormholes and Warped Spacetimes

Abstract

The Carminati and McLenaghan (CM) curvature invariants are powerful tools for probing spacetimes. Henry et al. formulated a method of plotting the CM curvature invariants to study black holes. The CM curvature invariants are scalar functions of the underlying spacetime. Consequently, they are independent of the chosen coordinates and characterize the spacetime. For Class B 1 spacetimes, there are four independent CM curvature invariants: R, r 1 , r 2 , and w 2 . Lorentzian traversable wormholes and warp drives are two theoretical solutions to Einstein's field equations, which allow faster-than-light (FTL) transport. The CM curvature invariants are plotted and analyzed for these specific FTL spacetimes: (i) the Thin-Shell Flat-Face wormhole, (ii) the Morris-Thorne wormhole, (iii) the Thin-Shell Schwarzschild wormhole, (iv) the exponential metric, (v) the Alcubierre metric at constant velocity, (vi) the Natário metric at constant velocity, and (vii) the Natário metric at an accelerating velocity.Plots of the wormhole CM invariants confirm their traversability and show how to distinguish the wormholes. The warp drive CM invariants reveal key features such as a flat harbor in the center of each warp bubble, a dynamic wake for each warp bubble, and rich internal structure(s) of each warp bubble.

Perfect fluid warp drive solutions with the cosmological constant

“…They also claimed that a warp field interferometer could not detect spacetime distortions. Mattingly et al [18,19] studied the curvature invariants characteristic of Natario and Alcubierre warp drives, whereas Mattingly [20] discussed further curvature invariants for warped spacetimes.…”