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Asymptotic flatness, reflection symmetry, and Birkhoff's theorem for R + R 2 actions containing quadratic torsion terms

1982; American Physical Society; Volume: 25; Issue: 2 Linguagem: Inglês

10.1103/physrevd.25.577

1538-4500

Richard T. Rauch,

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The proof of the Birkhoff-type theorem: For asymptotically flat O(3) spherically symmetric spacetime the unique solution of the vacuum field equations is the Schwarzschild solution with vanishing torsion, is extended to $R+{R}^{2}$ actions containing a quadratic torsion term. The simplifying power of the assumption of asymptotic flatness is severely degraded when reflection symmetry is not assumed, further underscoring the sensitivity of Riemann-Cartan theories to reflection symmetry, and inhibiting the proof of a similar theorem for SO(3) spherical symmetry.