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  Spin geometry and conservation laws in the Kerr spacetime

Andersson, L., Bäckdahl, T., & Blue, P. (2015). Spin geometry and conservation laws in the Kerr spacetime. In L. Bieri (Ed.), One hundred years of general relativity (Surveys in Differential Geometry, 20) (pp. 183-226). Boston: International Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-0001-8 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-3BC5-A
Genre: Book Chapter

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 Creators:
Andersson, Lars1, Author              
Bäckdahl, Thomas, Author
Blue, Pieter, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,
 Abstract: In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis is the existence of a valence $(2,0)$ Killing spinor, which we use to construct symmetry operators and conserved currents as well as a new energy momentum tensor for the Maxwell test fields on a class of spacetimes containing the Kerr spacetime. We then outline how this new energy momentum tensor can be used to obtain decay estimated for Maxwell test fields. An important motivation for this work is the black hole stability problem, where fields with non-zero spin present interesting new challenges. The main tool in the analysis is the 2-spinor calculus, and for completeness we introduce its main features.

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 Dates: 2015-04-082015
 Publication Status: Published in print
 Pages: 30 pages. To appear in the volume "The Centenary of General Relativity" in "Surveys in Differential Geometry", edited by Lydia Bieri and Shing-Tung Yau, in the series "Surveys in Differential Geometry"
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 Identifiers: arXiv: 1504.02069
DOI: 10.4310/SDG.2015.v20.n1.a8
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Title: One hundred years of general relativity (Surveys in Differential Geometry, 20)
Source Genre: Book
 Creator(s):
Bieri, L., Editor
Yau , S.-T. , Author
Affiliations:
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Publ. Info: Boston : International Press
Pages: - Volume / Issue: 20 Sequence Number: - Start / End Page: 183 - 226 Identifier: -