Appell rings in general relativity
Abstract
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 spacetimes 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 1989
 DOI:
 10.1088/02649381/6/7/005
 Bibcode:
 1989CQGra...6..977G
 Keywords:

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