Gravitational eigenstates in weak gravity II: further approximate
  methods for decay rates
  This paper develops further approximate methods for obtaining the dipole
matrix elements and corresponding transition and decay rates of the high-n,
high-l gravitational eigenstates. These methods include (1) investigation of
the polar spreads of the angular components of the high-n, high-l eigenstates
and the effects these have on the limiting values of the angular components of
the dipole matrix elements in the case of large l and m and (2) investigation
of the rapid cut off and limited width of the low-p, high-n radial
eigenfunctions, and the development of an equation to determine the width,
position and oscillatory behaviour of those eigenfunctions in cases of
arbitrarily large values of n, l and p. The methods have wider applicability
than dipole transition rate estimates and may be also used to determine limits
on the rates for more general interactions. Combining the methods enables the
establishment 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 many
channels available for decay. The results continue to support the hypothetical
existence of a specialized set of high-n, low-p gravitational eigenfunctions
that are invisible and stable, both with respect to electromagnetic decay and
gravitational collapse, making them excellent dark matter candidates.
