Localizing energy in Fierz-Lanczos theory

2020/04/07 by Jacek Jezierski, Jerzy Kijowski, Marian Wiatr · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Exact solutions in general relativity #Gravitation #Hamiltonian (control theory) #Lanczos resampling #Lanczos tensor #Massless particle #Mathematical physics #Mathematics #Physics #Quantum electrodynamics #Quantum mechanics #Relativity and Gravitational Theory #Tensor field #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.102.024015

published in Physical review. D/Physical review. D. 102(2) (American Physical Society) · 25 pages

arxiv created 2020/04/07 · openalex publication_date 2020/07/06 · arxiv updated 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We calculate energy carried by a massless spin-2 field using Fierz-Lanczos representation of the theory. For this purpose Hamiltonian formulation of the field dynamics is thoroughly analyzed. Final expression for the energy is very much analogous to the Maxwell energy in electrodynamics (spin-1 field) and displays the locality property. This quantity, known as a ``superenergy'' in gravity theory, differs considerably from the well understood gravitational field energy (represented in linear gravity by the quadratic term in Taylor expansion of the Arnowitt-Deser-Misner energy) which cannot be localized.

Citations

• The relation between metric and spin-2 formulations of linearized Einstein theory
• The Lanczos potential as a spin-2 field
• The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions
• Spin-2 field theory in curved spacetime
• Linearized general relativity and the Lanczos potential
• Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature
• On the relativistic theory of force-free particles with any spin
• Energy in gravitation and Noether’s theorems*