Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991nyasa.631..194m&link_type=abstract
(Nonlinear problems in relativity and cosmology; Proceedings of the 6th Florida Workshop in Nonlinear Astronomy, Gainesville, Oc
Astronomy and Astrophysics
Astronomy
1
Einstein Equations, Newton Theory, Poisson Equation, Relativity, Schwarzschild Metric, Equations Of Motion, Potential Energy, Reissner-Nordstrom Solution
Scientific paper
Recent developments are reviewed on the locally conformal invariant fourth-order theory of gravity that has recently been advanced as a potential candidate alternative to the standard second-order Einstein theory. Five new exact solutions to the theory are presented: the fourth-order analogs of the exterior Schwarzschild, the interior Schwarzschild, the exterior Reissner-Nordstrom, the exterior Kerr, and the exterior Kerr-Newman solutions. Each of these solutions is found to be conceptually different in structure form its second-order counterpart. In particular, the metric outside of a static spherically symmetric matter distribution is found to possess a linearly rising potential term in addition to the standard 1/r Newtonian term of the second-order exterior Schwarzschild solution. The interior problem associated with this solution reduces exactly to a simple Poisson equation with a fourth-order operator rather than with the familiar second-order one.
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