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The Carter tensor is a Killing tensor of the Kerr-Newman spacetime, and its existence implies the separability of the wave equation. Nevertheless, the Carter operator is known to commute with the D’Alembertian only in the case of a Ricci-flat metric. We show that, even though the Kerr-Newman spacetime satisfies the non-vacuum Einstein-Maxwell equations, its curvature and electromagnetic tensors satisfy peculiar properties which imply that the Carter operator still commutes with the wave equation. This feature allows to adapt to Kerr-Newman the physical-space analysis of the wave equation in Kerr by Andersson-Blue [4], which avoids frequency decomposition of the solution by precisely making use of the commutation with the Carter operator. We also extend the mathematical framework of physical-space analysis to the case of the Einstein-Maxwell equations on Kerr-Newman spacetime, representing coupled electromagnetic-gravitational perturbations of the rotating charged black hole. The physical-space analysis is crucial in this setting as the coupling of spin- 1 and spin-2 fields in the axially symmetric background prevents the separation in modes as observed by Chandrasekhar [19], and therefore represents an important step towards an analytical proof of the stability of the Kerr-Newman black hole.
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This content will become publicly available on May 1, 2026
Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
Two modern programs involving analogies between general relativity and electro-magnetism, gravito-electromagnetism (GEM) and the classical double copy (CDC), induce electromagnetic potentials from specific classes of spacetime metrics. We demonstrate such electromagnetic potentials are typically gauge equivalent to Killing vectors present in the spacetime, long known themselves to be analogous to electromagnetic potentials. We utilize this perspective to relate the Type D Weyl double copy to the Kerr-Schild double copy without appealing to specific coordinates. We analyze the typical assumptions taken within Kerr-Schild double copies, emphasizing the role Killing vectors play in the construction. The basis of the GEM program utilizes comparisons of tidal tensors between GR and EM; we perform a more detailed analysis of conditions necessary for equivalent tidal tensors between the theories, and note they require the same source prescription as the classical double copy. We discuss how these Killing vector potentials relate to the Weyl double copy, in particular there must a relation between the field strength formed from the Killing vector and the Weyl tensor. We consider spacetimes admitting a Killing-Yano tensor which provide a particularly insightful example of this correspondence. This includes a broad class of spacetimes, and provides an explanation for observations regarding the splitting of the Weyl tensor noted when including sources.
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- Award ID(s):
- 2210562
- PAR ID:
- 10618327
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 5
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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