Physics & Astronomy Faculty Publications
Document Type
Article
Publication Date
10-2026
Abstract
In this work we will investigate the structures of invariants within the class of plane waves in linearized General Relativity, to introduce a new approach to determine the linearized gauge invariants encoding the polarization of the plane waves. The Newman–Penrose (NP) formalism is traditionally used to analyze the polarization content of gravitational waves, while the gauge-invariant Bardeen formalism provides a complementary description based on the irreducible scalar, vector, and tensor perturbations of the metric. We will apply the Bardeen formalism to compute all scalar, vector, and tensor gauge-invariant variables explicitly and verify that only the two transverse–traceless tensor modes survive. We then compare these Bardeen variables with curvature-based invariants constructed using the linearized Cartan–Karlhede (CK) algorithm. Although one might anticipate a correspondence, our analysis shows that the CK invariants do not capture the polarization modes: the Weyl tensor possesses only a single non-zero Newman–Penrose scalar and the CK algorithm terminates without producing invariants that distinguish the ⊕ and ⊗ states. However, by computing invariant quantities obtained from the translational Killing vector fields of the Minkowski background that are retained under linear perturbation, we provide an algorithmic approach that reproduces the same physical tensor degrees of freedom captured by the Bardeen variables. The algorithm is a new result which is expected to be applicable to determine linearized gauge invariants for any linearized gravity solution admitting symmetries.
Recommended Citation
Radhakrishnan, Ramesh, David McNutt, Delaram Mirfendereski, Eric Davis, William Julius, and Gerald Cleaver. "Where are linearized gauge invariants encoded for plane waves in linearized gravity." The European Physical Journal C 86, no. 10 (2026): 1183. https://doi.org/10.1140/epjc/s10052-026-16355-y
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
The European Physical Journal C
DOI
10.1140/epjc/s10052-026-16355-y
Comments
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.