  The existence of self-gravito-acoustic (SGA) shock signals (SSs) associated
with negative self-gravitational potential in the perturbed state of the
astrophysical compact objects (ACOs) (viz. white dwarfs, neutron stars, black
holes, etc.) is predicted for the first time. A modified Burgers equation (MB),
which is valid for both planar and non-planar spherical geometries, by the
reductive perturbation method. It is shown that the longitudinal viscous force
acting in the medium of any ACO is the source of dissipation, and is
responsible for the formation of these SGA SSs. The time evolution of these SGA
SSs is also shown for different values (viz. $0.5$, $1$, and $2$ ) of the ratio
of nonlinear coefficient to dissipative coefficient in the MB equation. The
theory presented here is so general that it can be applied in any ACO of planar
or non-planar spherical shape.
