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This paper develops further approximate methods for obtaining the dipolematrix elements and corresponding transition and decay rates of the high-n,high-l gravitational eigenstates. These methods include (1) investigation ofthe polar spreads of the angular components of the high-n, high-l eigenstatesand the effects these have on the limiting values of the angular components ofthe dipole matrix elements in the case of large l and m and (2) investigationof the rapid cut off and limited width of the low-p, high-n radialeigenfunctions, and the development of an equation to determine the width,position and oscillatory behaviour of those eigenfunctions in cases ofarbitrarily large values of n, l and p. The methods have wider applicabilitythan dipole transition rate estimates and may be also used to determine limitson the rates for more general interactions. Combining the methods enables theestablishment of upper limits to the total dipole decay rates of many high-n,low-p states on the state diagram to be determined, even those that have manychannels available for decay. The results continue to support the hypotheticalexistence of a specialized set of high-n, low-p gravitational eigenfunctionsthat are invisible and stable, both with respect to electromagnetic decay andgravitational collapse, making them excellent dark matter candidates.

Gravitational eigenstates in weak gravity II: further approximate methods for decay rates