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Phys. Rev. D 80, 024021 (2009) [14 pages]

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

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David Brizuela
Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain

José M. Martín-García
Laboratoire Univers et Théories, Observatoire de Paris, CNRS, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France, and Institut d’Astrophysique de Paris, Université Pierre et Marie Curie, CNRS, 98 bis boulevard Arago, 75014 Paris, France

Manuel Tiglio
Center for Scientific Computation and Mathematical Modeling and Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland, 20742, USA

Received 6 March 2009; published 17 July 2009

Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative (l≥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 nonlinear effects in gravitational radiation, the second-order stability of the Schwarzschild spacetime, or the geometry of the black hole horizon.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.80.024021
DOI:
10.1103/PhysRevD.80.024021
PACS:
04.25.Nx, 04.30.−w
 
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