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New identities for linearized gravity on the Kerr spacetime
Albert Einstein Institute, Potsdam, Germany.
Albert Einstein Institute, Potsdam, Germany.
Örebro University, School of Science and Technology. Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden; The University of Edinburgh, Edinburgh, United Kingdom.ORCID iD: 0000-0003-3240-2445
2019 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 99, no 4, article id 044043Article in journal (Refereed) Published
Abstract [en]

In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor M-ab which solves the linearized Einstein equations. The identity makes this manifest by relating M-ab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of M-ab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.

Place, publisher, year, edition, pages
American Physical Society, 2019. Vol. 99, no 4, article id 044043
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:oru:diva-73123DOI: 10.1103/PhysRevD.99.044043ISI: 000459581200003Scopus ID: 2-s2.0-85062344661OAI: oai:DiVA.org:oru-73123DiVA, id: diva2:1296201
Funder
Knut and Alice Wallenberg Foundation
Note

Funding Agency:

EP/J011142/1

Available from: 2019-03-14 Created: 2019-03-14 Last updated: 2019-03-14Bibliographically approved

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Bäckdahl, Thomas

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