  In this paper, we first discuss a series of important but puzzling physical
mechanisms concerning the energy source, various kinds of core collapsed
supernovae explosion mechanisms during central gravitational collapse in
astrophysics. We also discuss the puzzle of possible association of
$\gamma$-ray burst with gravitational wave perturbation, the heat source for
the molten interior of the core of the earth and finally the puzzling problem
of the cooling of white dwarfs. We then make use of the estimations for the
space flux of magnetic monopoles (hereafter MMs) and nucleon decay induced by
MMs (called the Rubakov-Callen(RC) effect) to obtain the luminosity due to the
RC effect. In terms of the formula for this RC luminosity, we present a unified
treatment for the heat source of the Earth's core, the energy source for the
white dwarf interior, various kinds of core collapsed supernovae (Type II
Supernova (SNII), Type Ib Supernova (SNIb), Type Ic Supernova (SNIc), Super
luminous supernova (SLSN)), and the production mechanism for $\gamma$-ray
burst. This unified model can also be used to reasonably explain the possible
association of the short $\gamma$-ray burst detected by the Fermi $\gamma$-ray
Burst Monitoring Satellite (GBM) with the LIGO gravitational wave event
GW150914 in September 2015.
