The conformal Killing spinor initial data equations

E. Gasperín, J. L. Williams

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number104615
JournalJournal of Geometry and Physics
Early online date4 Jul 2022
Publication statusPublished - 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.


  • 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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