Appell rings in general relativity

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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.

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Classical and Quantum Gravity

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