  We present here the linear regime of the Einstein's field equations in the
characteristic formulation. Through a simple decomposition of the metric
variables in spin-weighted spherical harmonics, the field equations are
expressed as a system of coupled ordinary differential equations. The process
for decoupling them leads to a simple equation for $J$ - one of the Bondi-Sachs
metric variables - known in the literature as the master equation. Then, this
last equation is solved in terms of Bessel's functions of the first kind for
the Minkowski's background, and in terms of the Heun's function in the
Schwarzschild's case. In addition, when a matter source is considered, the
boundary conditions across the time-like world tubes bounding the source are
taken into account. These boundary conditions are computed for all multipole
modes. Some examples as the point particle binaries in circular and eccentric
orbits, in the Minkowski's background are shown as particular cases of this
formalism.
