A Quadratic Spinor Lagrangian for General Relativity

Abstract

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)

5 pages (Plain TeX), NCU-GR-94-QSLG

References in corpus (2)

• Another positivity proof and gravitational energy localizations
• Some Spinor-Curvature Identities

Cited by in corpus (13)

• Quasilocal quantities for GR and other gravity theories
• From Dirac spinor fields to ELKO
• The quadratic spinor Lagrangian, axial torsion current, and generalizations
• Quasilocal Energy-Momentum for Geometric Gravity Theories
• The quadratic spinor Lagrangian is equivalent to the teleparallel theory
• ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity
• Spinor One-forms as Gravitational Potentials
• Origin of the Immirzi Parameter
• Quasilocal Energy for Spin-net Gravity
• Gravitation as a Supersymmetric Gauge Theory
• Conservation laws for vacuum tetrad gravity
• Optimal Choices of Reference for a Quasi-local Energy: Spherically Symmetric Spacetimes
• On energy for accelerating observers in black hole spacetimes