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Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

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arxiv gr-qc/0207070 v2 pith:DI6AKYZO submitted 2002-07-18 gr-qc hep-th

Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

classification gr-qc hep-th
keywords newtoniandimensionsgeneralizationgravitymetricrelativistictheoryvacuum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.

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