A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole

Abstract

Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative $(l\ge 2)$ second-order perturbations of a Schwarzschild black hole. In particular, we construct the second order Zerilli and Regge-Wheeler equations under the presence of any two first-order modes, reconstruct the perturbed metric in terms of the master scalars, and compute the radiated energy at null infinity. The results of this paper enable systematic studies of generic second order perturbations of the Schwarzschild spacetime. In particular, studies of mode-mode coupling and non-linear effects in gravitational radiation, the second-order stability of the Schwarzschild spacetime, or the geometry of the black hole horizon.

14 pages

References in corpus (3)

• Second and higher-order quasi-normal modes in binary black hole mergers
• High-order gauge-invariant perturbations of a spherical spacetime
• Regular second order perturbations of binary black holes: The extreme mass ratio regime

Cited by in corpus (1)

• Nonlinear radial oscillations of neutron stars