Spinor Structure of Space-Times in General Relativity. I

1968/11/01 by Robert Geroch · 1 voice · 10 citations
Physics and Astronomy · #Relativity and Gravitational Theory #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories

paper · doi:10.1063/1.1664507

openalex publication_date 1968/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

In order to define spinor fields on a space-time M, it is necessary first to endow M with some further structure in addition to its Lorentz metric. This is the spinor structure. The definition and the elementary implications of the existence of a spinor structure are discussed. It is proved that a necessary and sufficient condition for a noncompact space-time M to admit a spinor structure is that M have a global field of orthonormal tetrads.

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Discussions

• In Geroch (1968) , Geroch proved the following result in the appendix for smooth manifolds (not assumed to be paracompact) with a Lorentz metric: Let $M$ be a connected smooth manifold with a smooth L [stackexchange, 2 points]

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