All torsion-free spherical vacuum solutions of the quadratic Poincare gauge theory of gravity

Mathematics – Logic

Scientific paper

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Cosmology, Gauge Theory, Gravitation Theory, Quadratic Equations, Poincare Problem, Relativity, Schwarzschild Metric, Space-Time Functions, Vacuum

Scientific paper

The complete torsion-free spherically symmetric vacuum solutions of the theory of gravity proposed by Hehl et al. (1978) are obtained analytically and characterized. The solutions are shown to correspond to either Schwarzschild metrics (including a gravitational confinement potential when the cosmological constant Lambda is less than zero), Narai-Bertotti metrics, or conformally flat metrics (including some asymptotically flat but nonstationary solutions). The relationships of the theory of Hehl et al. to those of Eddington (1924), Nordstrom (1913), Einstein (1917, with cosmological constant), and Yang (1974) are explored.

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