| 1. |
- Aksteiner, S., et al.
(author)
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New identities for linearized gravity on the Kerr spacetime
- 2019
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In: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 99:4
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Bossard, Guillaume, et al.
(author)
-
Generalised diffeomorphisms for E9
- 2017
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In: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022-
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Journal article (peer-reviewed)abstract
- We construct generalised diffeomorphisms for E9 exceptional field theory. The trans- formations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism alge- bra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordi- nate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk–Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.
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