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تسجيل مستخدم جديدSecond Order Perturbations of Kerr Black Holes: Reconstruction of the Metric
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Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading order nonlinear gravitational wave interactions around a Kerr black hole. We describe the formalism used to derive the equations for second order perturbations. We develop a procedure that allows us to reconstruct the first order metric perturbation solely from knowledge of the solution to the first order Teukolsky equation, without the need of Hertz potentials. Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first order quasi-normal modes of Kerr. In a companion paper, we present a numerical implementation of these ideas.
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Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spaceti
mes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the linearly perturbed Weyl scalar $Psi_4^{(1)}$, followed by direct reconstruction of the spacetime metric from $Psi_4^{(1)}$, and then solve for the dynamics of the second order perturbed Weyl scalar $Psi_4^{(2)}$. This code is a first step toward a more general purpose second order code, and we outline how our basic approach could be further developed to address current questions of interest, including extending the analysis of ringdown in black hole mergers to before the linear regime, exploring gravitational wave turbulence around near-extremal Kerr black holes, and studying the physics of extreme mass ratio inspiral.
Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars $psi_0$ or $psi_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated wit
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The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise a
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