Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum

Abstract

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a gravitational wave does make sense also beyond the linear approximation.

14 pages. arXiv admin note: text overlap with arXiv:1701.07804; v2: 16 pages, minor changes in the text, misprint in Eqs. (39,62,63,67,68) corrected, Eq. (70) added, 5 references added

References in corpus (5)

• Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
• A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
• Second and higher-order perturbations of a spherical spacetime
• Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform
• Anti-de Sitter geon families

Cited by in corpus (8)

• Quantum signatures in nonlinear gravitational waves
• Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
• Anti-de Sitter geon families
• Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe
• Time-periodicities in holographic CFTs
• Vacuum axisymmetric gravitational collapse revisited: preliminary investigation
• Gravitational systems in asymptotically anti-de Sitter space-times
• On the propagation of gravitational waves in matter-filled Bianchi I universe