Einstein's theory in a three-dimensional space-time

Details Einstein's theory in a three-dimensional space-time Einstein's theory in a three-dimensional space-time

Aug 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16..751g&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 16, Aug. 1984, p. 751-775. Research supported by the University of Uta

Mathematics

Logic

159

Dimensions, Gravitation Theory, Quantum Theory, Relativity, Space-Time Functions, Big Bang Cosmology, Canonical Forms, Cosmic Dust, Gravitational Collapse, Newton Theory, Riemann Manifold, Stellar Models

Scientific paper

As a preparation for studying quantum models, we analyze unusual features of Einstein's theory of gravitation in a three-dimensional space-time. In three dimensions, matter curves space-time only locally and the gravitational field has no dynamical degrees of freedom. The standard correspondence of Einstein's theory with Newton's theory breaks down. A dust distribution moves without any geodesic deviation between the particles. The cosmological models and relativistic stars behave in a qualitatively different way from their Newtonian counterparts. These features are important for the correct understanding of mini-superspace models.

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