A Closer Look at Nat\'ario's Zero-Expansion Warp Drive
Jos\'e Rodal

TL;DR
This paper provides a detailed analysis of Natário's zero-expansion warp drive spacetime, revealing its Petrov type, the significance of Weyl curvature, and comparing its physical viability to Alcubierre's model, ultimately questioning its practicality.
Contribution
It classifies Natário's warp drive as Petrov type I, analyzes curvature invariants including Weyl, visualizes physical quantities, and compares its curvature magnitude to Alcubierre's, challenging claims of its realism.
Findings
Natário's spacetime is Petrov type I.
Weyl curvature plays a significant role near the warp bubble.
Curvature invariants are 35 times larger than Alcubierre's, reducing viability.
Abstract
We conduct a detailed analysis of Nat'{a}rio's ``zero-expansion'' warp drive spacetime, focusing on scalar curvature invariants within the 3+1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Nat'{a}rio's spacetime, which has not been previously determined in the literature. We prove that Nat'{a}rio's spacetime is Petrov type I, not fitting the Class B warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein's scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius.…
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Noncommutative and Quantum Gravity Theories
