Non-linear perturbations of a spherically collapsing star

Mathematics

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Theory Of Quantized Fields, Gravitational Waves: Theory, Ordinary And Partial Differential Equations, Boundary Value Problems

Scientific paper

Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

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