Thin Shell with Fictitious Motions
Résumé
We show that a spherical thin shell with fictitious radial motions can mimic the gravitational effects of a massive spherical thin shell. These fictitious radial motions (either with a uniform velocity or oscillate about the thin shell) are not physical motions of the thin shell. Instead, we use their hypothetical effects on time and distance measurements to define the spacetime metric on the surface of the timelike thin shell. The system with fictitious motions is spherically symmetric with time translational and time reflection symmetries. The external spacetime outside the thin shell is static and satisfies the Schwarzschild solution for the gravitational field of a spherically symmetric mass.
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