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Peer-reviewedCC BY 4.0The European Physical Journal C

Where are linearized gauge invariants encoded for plane waves in linearized gravity

  • Ramesh Radhakrishnan1,2
  • David McNutt1,3
  • Delaram Mirfendereski1,4
  • Eric Davis1,5
  • William Julius1,6
  • Gerald Cleaver1,2
6 affiliations
  1. 1Center for Astrophysics, Space Physics and Engineering Research (CASPER)
  2. 2Baylor University
  3. 3Royal Norwegian Naval Academy
  4. 4The University of Texas Rio Grande Valley (UTRGV)
  5. 5SUNY-Albany
  6. 6St. Cloud State University
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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.

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Cite

BibTeXRIS
BibTeX
@article{radhakrishnan2026where,
  title = {{Where are linearized gauge invariants encoded for plane waves in linearized gravity}},
  author = {Ramesh Radhakrishnan and David McNutt and Delaram Mirfendereski and Eric Davis and William Julius and Gerald Cleaver},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16355-y},
  url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16355-y},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Where are linearized gauge invariants encoded for plane waves in linearized gravity
AU  - Ramesh Radhakrishnan
AU  - David McNutt
AU  - Delaram Mirfendereski
AU  - Eric Davis
AU  - William Julius
AU  - Gerald Cleaver
PY  - 2026
DA  - 2026/10/19
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16355-y
UR  - https://link.springer.com/article/10.1140/epjc/s10052-026-16355-y
AB  - 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.
SN  - 1434-6044
SN  - 1434-6052
ER  -