A Fundamental Equation for Gravitational Wave and Its Analogues in Type D Spacetimes

TL;DR

This paper introduces a universal equation for gravitational perturbations in Type D spacetimes, applicable to various black holes and massless fields, providing a new framework beyond Kerr-specific equations.

Contribution

It presents a novel, metric-independent equation for gravitational perturbations and massless fields, unifying their description across different black hole spacetimes.

Findings

The equation applies universally to Type D spacetimes.

Massless fields with spin s<2 obey a gravitational wave-like equation.

The coefficients have explicit physical significance.

Abstract

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.