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between the two cases: the excited monopole is not an arbitrary field: it is carefully chosen by the dynamics of the problem, and may be viewed as a fine tuned field; the injected monopole is arbitrary, and is not fine tuned to lead to a different late–time decay rate. 

## IV. EXCITATION OF “UP” MODES 

Most interest has been devoted to finding the decay rate of the slowest decaying mode, for obvious reasons. Specif- ically, the slowest decaying mode determines the late–time behavior of the full field. As lower multipole modes typically have a slower decay rate, most interest has naturally focused on the excitation of “down” modes, specifically the excitation of lower multipole modes starting with higher multipole modes. 

Here, we are interested in the converse, i.e., in the excitation and decay rate of “up” modes, i.e., the excitation and decay rate of a higher multipole mode than the one initially excited. Such modes are typically sub-dominant, and do not dominate the late–time behavior of the full field. Our interest in the “up” modes is therefore only tangentially 

