Appell rings in general relativity

Details Appell rings in general relativity Appell rings in general relativity

Jul 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6..977g&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, July 1, 1989, p. 977-985. Research supported by CONICOR and CONICET.

Mathematics

14

Einstein Equations, Relativity, Laplace Equation, Newton Theory, Rings (Mathematics), Vacuum

Scientific paper

Exact static solutions of the vacuum Einstein equations obtained from the Appell ring solution to the Laplace equation are analyzed. A Newtonian analysis is performed, and it is shown that the Appell solution may be interpreted as the field of a shell of infinite negative total mass bordered by a ring of infinite positive total mass. This situation can be reproduced in general relativity, but a different interpretation, not requiring the shell as a source, is also possible, in which two space-times are pasted through the ring. The superposition of a particle with an Appell ring is also considered, and in this case the shell interpretation is found to be inconsistent.

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