  The oscillating gravitational field of an oscillaton of finite mass M causes
it to lose energy by emitting classical scalar field waves, but at a rate that
is non-perturbatively tiny for small GMm, where m is the scalar field mass:
d(GM)/dt ~ -3797437.776333015 e^[-39.433795197160163/(GMm)]/(GMm)^2.
Oscillatons also decay by the quantum process of the annihilation of scalarons
into gravitons, which is only perturbatively small in GMm, giving by itself
d(GM)/dt ~ - 0.008513223934732692 G m^2 (GMm)^5. Thus the quantum decay is
faster than the classical one for Gmm < 39.4338/[ln(1/Gm^2)}-7ln(GMm)+19.9160].
The time for an oscillaton to decay away completely into free scalarons and
gravitons is ~ 2/(G^5 m^11) ~ 10^324 yr (1 meV/m)^11. Oscillatons of more than
one real scalar field of the same mass generically asymptotically approach a
static-geometry U(1) boson star configuration with GMm = GM_0 m, at the rate
d(GM/c^3)/dt ~ [(C/(GMm)^4)e^{-alpha/(GMm)}+Q(m/m_{Pl})^2(GMm)^3]
[(GMm)^2-(GM_0 m)^2], with GM_0 m depending on the magnitudes and relative
phases of the oscillating fields, and with the same constants C, alpha, and Q
given numerically above for the single-field case that is equivalent to GM_0 m
= 0.
