The conformal Killing spinor initial data equations

E. Gasperín; J. L. Williams

doi:10.1016/j.geomphys.2022.104615

The conformal Killing spinor initial data equations

E. Gasperín, J. L. Williams

Department of Mathematical Sciences

University of Lisbon

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field equations are used in our derivation allows for the possibility of the initial hypersurface S intersecting non-trivially with (or even being a subset of) null infinity I. For conciseness, these conditions are derived assuming that the initial hypersurface is spacelike. Hence, in particular, these conformal Killing spinor initial data equations encode necessary and sufficient conditions for the existence of a Killing spinor in the development of asymptotic initial data on spacelike components of I.

Original language	English
Article number	104615
Journal	Journal of Geometry and Physics
Volume	179
Early online date	4 Jul 2022
DOIs	https://doi.org/10.1016/j.geomphys.2022.104615
Publication status	Published - 30 Sept 2022

Bibliographical note

Funding Information:
We would like to thank Juan A. Valiente Kroon, David Hilditch and Justin Feng for helpful discussions. Additionally, we thank the anonymous referee for the feedback provided. E. Gasperín acknowledges support from Consejo Nacional de Ciencia y Tecnología (Mexico) —CONACyT studentship 494039/218141 — in the early stages of this work and from Fundação para a Ciência e a Tecnologia (Portugal) — FCT-2020.03845 . CEECIND— during its completion. J. L. Williams acknowledges support from the COST Action CA16104 - Gravitional waves, black holes (GWniverse) STSM ECOST-STSM.

Funding

We would like to thank Juan A. Valiente Kroon, David Hilditch and Justin Feng for helpful discussions. Additionally, we thank the anonymous referee for the feedback provided. E. Gasperín acknowledges support from Consejo Nacional de Ciencia y Tecnología (Mexico) —CONACyT studentship 494039/218141 — in the early stages of this work and from Fundação para a Ciência e a Tecnologia (Portugal) — FCT-2020.03845 . CEECIND— during its completion. J. L. Williams acknowledges support from the COST Action CA16104 - Gravitional waves, black holes (GWniverse) STSM ECOST-STSM.

Keywords

Conformal boundary
Conformal Einstein field equations
Kerr-de Sitter spacetime
Killing initial data
Killing spinors
Petrov type D spacetimes

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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Cite this

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title = "The conformal Killing spinor initial data equations",

abstract = "We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field equations are used in our derivation allows for the possibility of the initial hypersurface S intersecting non-trivially with (or even being a subset of) null infinity I. For conciseness, these conditions are derived assuming that the initial hypersurface is spacelike. Hence, in particular, these conformal Killing spinor initial data equations encode necessary and sufficient conditions for the existence of a Killing spinor in the development of asymptotic initial data on spacelike components of I.",

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AU - Williams, J. L.

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N2 - We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field equations are used in our derivation allows for the possibility of the initial hypersurface S intersecting non-trivially with (or even being a subset of) null infinity I. For conciseness, these conditions are derived assuming that the initial hypersurface is spacelike. Hence, in particular, these conformal Killing spinor initial data equations encode necessary and sufficient conditions for the existence of a Killing spinor in the development of asymptotic initial data on spacelike components of I.

AB - We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field equations are used in our derivation allows for the possibility of the initial hypersurface S intersecting non-trivially with (or even being a subset of) null infinity I. For conciseness, these conditions are derived assuming that the initial hypersurface is spacelike. Hence, in particular, these conformal Killing spinor initial data equations encode necessary and sufficient conditions for the existence of a Killing spinor in the development of asymptotic initial data on spacelike components of I.

KW - Conformal boundary

KW - Conformal Einstein field equations

KW - Kerr-de Sitter spacetime

KW - Killing initial data

KW - Killing spinors

KW - Petrov type D spacetimes

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ER -

The conformal Killing spinor initial data equations

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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