Appell rings in general relativity
The authors analyse exact static solutions of the vacuum Einstein equations obtained from the Appell ring solution to the Laplace equation. They first perform a Newtonian analysis and show 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 pasting two spacetimes 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 Source (Journal or Book title)
Classical and Quantum Gravity
Gleiser, R., & Pullin, J. (1989). Appell rings in general relativity. Classical and Quantum Gravity, 6 (7), 977-985. https://doi.org/10.1088/0264-9381/6/7/005