Spinor formulation of topologically massive gravity

Details Spinor formulation of topologically massive gravity Spinor formulation of topologically massive gravity

1998-12-28

arxiv.org/abs/gr-qc/9812090v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

An expanded version of paper published in Classical and Quantum Gravity 12 (1995) 2913

Scientific paper

10.1088/0264-9381/12/12/009

In the framework of real 2-component spinors in three dimensional space-time we present a description of topologically massive gravity (TMG) in terms of differential forms with triad scalar coefficients. This is essentially a real version of the Newman-Penrose formalism in general relativity. A triad formulation of TMG was considered earlier by Hall, Morgan and Perjes, however, due to an unfortunate choice of signature some of the spinors underlying the Hall-Morgan-Perjes formalism are real, while others are pure imaginary. We obtain the basic geometrical identities as well as the TMG field equations including a cosmological constant for the appropriate signature. As an application of this formalism we discuss the Bianchi Type $VIII - IX$ exact solutions of TMG and point out that they are parallelizable manifolds. We also consider various re-identifications of these homogeneous spaces that result in black hole solutions of TMG.

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