Abstract
Scalar, electromagnetic, and gravitational test fields in the Schwarzschild background are examined with the help of the general retarded solution of a single master wave equation. The solution for each multipole is generated by a single arbitrary function of retarded time, the retarded multipole moment. We impose only those restrictions on the time dependence of the multipole moment which are required for physical regularity. We find physically well-behaved solutions which (i) do not satisfy the Penrose peeling theorems at past null infinity and/or (ii) do not have well-defined Newman-Penrose quantities. Even when the NP quantities exist, they are not measurable; they represent an ``average'' multipole moment over the infinite past, and their conservation is essentially trivial.
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