Linear perturbations of self-gravitating spherically symmetric configurations

Understand

We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity.

• The advantage of this formalism relies in the fact that it does not require a decomposition of the perturbations into spherical tensor harmonics.
• Furthermore, it does not assume the background to be vacuum, nor does it require its staticity.
• In the particular case of vacuum perturbations, we derive two master equations describing the propagation of arbitrary linear gravitational waves on a Schwarzschild black hole.