  It is well known that Teukolsky equation of gravitational perturbations
provides a powerful tool for the investigation of the ringdown phase of a
binary black hole merger, but it is applicable only for final configurations in
the Kerr cases. Here we introduce a new concept: the spin-coefficient
connection. Employing it and a new transformation function, we find that the
gravitational perturbations can be written as a single equation. Each
coefficients of this equation has explicit physical significance. More
importantly, the equation is universally applied to virtually any black hole
since it does not depend on specific metrics and coordinate system. We also
find that any massless field of nonzero spin $s<2$ obeys the gravitational
wave-like equation, which shows that the fields can be used as the analogue
models of gravitational wave.

General Relativity and Quantum Cosmology