| 1. |
- Aksteiner, Steffen, et al.
(author)
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A space-time calculus based on symmetric 2-spinors
- 2023
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In: General Relativity and Gravitation. - : Springer Science and Business Media LLC. - 0001-7701 .- 1572-9532. ; 55:3
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Journal article (peer-reviewed)abstract
- In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay within the class of symmetric spinors, no involved index manipulations are needed. In fact spinor indices are not needed in the formalism. It is also general because any covariant tensor expression in a 4-dimensional Lorentzian spacetime can be translated to this formalism. The computer algebra implementation SymSpin as part of xAct for Mathematica is also presented.
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| 2. |
- Aksteiner, Steffen, et al.
(author)
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All Local Gauge Invariants for Perturbations of the Kerr Spacetime
- 2018
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In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 121
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Journal article (peer-reviewed)abstract
- We present two complex scalar gauge invariants for perturbations of the Kerr spacetime defined covariantly in terms of the Killing vectors and the conformal Killing-Yano tensor of the background together with the linearized curvature and its first derivatives. These invariants are, in particular, sensitive to variations of the Kerr parameters. Together with the Teukolsky scalars and the linearized Ricci tensor, they form a minimal set that generates all local gauge invariants. We also present curvature invariants that reduce to the gauge invariants in the linearized theory.
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| 3. |
- Aksteiner, Steffen, et al.
(author)
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Compatibility Complex for Black Hole Spacetimes
- 2021
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In: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 384:3, s. 1585-1614
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Journal article (peer-reviewed)abstract
- The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (Aksteiner and Bäckdahl in Phys Rev Lett 121:051104, 2018) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from Aksteiner and Bäckdahl (Phys Rev Lett 121:051104, 2018) with the first compatibility operator from that complex.
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| 4. |
- 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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| 5. |
- Aksteiner, S., et al.
(author)
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Symmetries of linearized gravity from adjoint operators
- 2019
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In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 60:8
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Journal article (peer-reviewed)abstract
- Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and, in particular, the Kerr spacetime. One of them is of differential order four and coincides with a result of Cohen and Kegeles. The other one is a new operator of differential order six. The corresponding operator identities are based on the Teukolsky equation and the Teukolsky-Starobinsky identities, respectively. The method applies to other field equations as well, which is illustrated with the Maxwell equation. The resulting symmetry operators are connected to Hertz and Debye potentials as well as to the separability of the Teukolsky equation for both Maxwell and linearized gravity.
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| 6. |
- Andersson, Lars, et al.
(author)
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A new tensorial conservation law for Maxwell fields on the Kerr background
- 2017
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In: Journal of Differential Geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 105:2, s. 163-176
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Journal article (peer-reviewed)abstract
- A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.
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| 7. |
- Andersson, Lars Erik, et al.
(author)
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Decay of solutions to the Maxwell equation on the Schwarzschild background
- 2016
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In: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 33:8
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Journal article (peer-reviewed)abstract
- A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor H-ab defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current H-ab (partial derivative(t))(b). The tensor Hab vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.
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| 8. |
- Andersson, L., et al.
(author)
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Nonlinear Radiation Gauge for Near Kerr Spacetimes
- 2022
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In: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 396, s. 45-90
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Journal article (peer-reviewed)abstract
- In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction (Chrzanowski in Phys Rev D 11:2042-2062, 1975) on the Kerr background. It has been shown by Price et al. (Class Quantum Gravity 24:2367-2388, 2007) that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In (Andersson et al. Stability for linearized gravity on the Kerr spacetime, 2019), the ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.
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| 9. |
- Bäckdahl, Thomas, 1980, et al.
(author)
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A formalism for the calculus of variations with spinors
- 2016
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In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 57:2
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Journal article (peer-reviewed)abstract
- We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2, C)) 2-spinors as well as to space (i.e., SU(2, C)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors.
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| 10. |
- Bäckdahl, Thomas, 1980-
(author)
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Axisymmetric stationary solutions with arbitrary multipole moments
- 2007
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In: International Conference on General Relativity and Gravitation,2007.
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Conference paper (other academic/artistic)abstract
- In general relativity, multipole moments gives a coordinate independent description of stationary spacetimes. Although the notion of multipole moments was developed in the seventies, there are still some open questions. The major remaining problem is, whether there exist spacetimes with arbitrary a-priori specified multipole moments. In this talk, this problem is studied for the axisymmetric case. A necessary and sufficient condition on the multipole moments is given for existence of a solution. Thus proving that the multipole moments completely characterise the axisymmetric stationary solutions.
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