Spinor formulation of topologically massive gravity

Abstract

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.

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

References in corpus (2)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole

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• Basis for scalar curvature invariants in three dimensions
• Null Surface Thermodynamics in Topologically Massive Gravity
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• Impulsive gravitational waves in general massive 3D gravity
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