Article

# Observables and gauge invariance in the theory of nonlinear spacetime perturbations

Classical and Quantum Gravity (Impact Factor: 3.56). 12/1998; 16(7):L29. DOI: 10.1088/0264-9381/16/7/101

Source: arXiv

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**ABSTRACT:**We introduce N-parameter perturbation theory as a new tool for the study of nonlinear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to prove the main results concerning the consistency of the scheme to any perturbative order. Gauge transformations and conditions for gauge invariance at any required order can then be derived from a generating exponential formula via a simple Taylor expansion. We outline the relation between our novel formulation and previous developments.Physical Review D 09/2004; 70(6). · 4.69 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**At a time when galaxy surveys and other observations are reaching unprecedented sky coverage and precision, it seems timely to investigate the effects of general relativistic nonlinear dynamics on the growth of structures and on observations. Analytic inhomogeneous cosmological models are an indispensable way of investigating and understanding these effects in a simplified context. In this paper, we develop exact inhomogeneous solutions of general relativity with pressureless matter (dust, describing cold dark matter) and cosmological constant Lambda, which can be used to model an arbitrary initial matter distribution along one line of sight. In particular, we consider the second class Szekeres models with Lambda, and split their dynamics into a flat LambdaCDM background and exact nonlinear inhomogeneities, obtaining several new results. One single metric function Z describes the deviation from the background. We show that F, the time dependent part of Z, satisfies the familiar linear differential equation for delta, the first-order density perturbation of dust, with the usual growing and decaying modes. In the limit of small perturbations, delta≈F as expected, and the growth of inhomogeneities links up exactly with standard perturbation theory. In particular, we exhibit an exact conserved curvature variable, necessary for the existence of the growing mode, which is the nonlinear extension of the first-order curvature perturbation. We provide analytic expressions for the exact nonlinear delta and the growth factor in our models. For the case of over-densities, we find that, depending on the initial conditions, the growing mode may or may not lead to a pancake singularity, analogous to a Zel'dovich pancake. This is in contrast with the Lambda=0 pure Einstein-de Sitter background where, at any given point in comoving (Lagrangian) coordinates, pancakes will always occur. Analyzing the covariant variables associated with the space-time, we derive the associated dynamical system, which we are able to decouple and reduce to two differential equations, one for OmegaLambda representing the background dynamics, and one for delta describing the dynamics of the inhomogeneities. Our models are Petrov type D, which we show by explicitly deriving the only nonzero Weyl scalar Psi2, which does not depend on Lambda. Since this is the only Weyl contribution to the geodesic deviation equation, Lambda can only contribute to lensing through its contribution to the background expansion.Physical review D: Particles and fields 01/2011; 83. - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the generation of electromagnetic radiation by gravitational waves interacting with a strong magnetic field in the vicinity of a vibrating Schwarzschild black hole. Such an effect may play an important role in gamma-ray bursts, supernovae, and in particular their afterglows. It may also provide an electromagnetic counterpart to gravity waves in many situations of interest, enabling easier extraction and verification of gravity wave waveforms from gravity wave detection. We set up the Einstein-Maxwell equations for the case of odd-parity gravity waves impinging on a static magnetic field as a covariant and gauge-invariant system of differential equations that can be integrated as an initial-value problem or analyzed in the frequency domain. We numerically investigate both of these cases. We find that the black hole ring-down process can produce substantial amounts of electromagnetic radiation from a dipolar magnetic field in the vicinity of the photon sphere.The Astrophysical Journal 12/2008; 613(1):492. · 6.73 Impact Factor

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