By M. Bartelmann, P. Schneider
Preprint.Abstract: We assessment idea and purposes of susceptible gravitational lensing. After summarisingFriedmann-Lemaitre cosmological types, we current the formalism of gravitational lensing and light-weight propagation in arbitrary space-times. We talk about how weak-lensing effectscan be measured. The formalism is then utilized to reconstructions of galaxy-cluster massdistributions, gravitational lensing via large-scale topic distributions, QSO-galaxy correlations triggered by means of susceptible lensing, lensing of galaxies through galaxies, and susceptible lensing of the cosmic microwave history.
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Additional resources for Weak Gravitational Lensing
There is no exact solution of Einstein’s field equations which describes a universe with density fluctuations, with the exception of a few very special cases such as the Swiss-Cheese model (Einstein & Strauss 1945). We therefore have to resort to approximation methods which start from identifying ‘small’ parameters of the problem, and expanding the relevant quantities into a Taylor series in these parameters. 38) where dτ = a−1 dt is the conformal time element, and Φ satisfies Poisson’s equation with source ∆ρ, the density enhancement or reduction relative to the mean cosmic density (Futamase 1989; Futamase & Sasaki 1989; Jacobs et al.
This exact result from General Relativity is of course not easily applied to practical calculations in general space-times, as one first has to calculate the null geodesic µ γ0 (λ), and from that the components of the tidal matrix have to be determined. However, as we shall show next, the equations attain rather simple forms in the case of weak gravitational fields. 23) to the situation of a homogeneous and isotropic universe, and to weak gravitational fields. 2, page 13), the source of shear F must vanish identically because of isotropy; otherwise preferred directions would exist.
Granted the validity of Einstein’s Theory of General Relativity, light propagates on the null geodesics of the space-time metric. However, most astrophysically relevant situations permit a much simpler approximate description of light rays, which is called gravitational lens theory; we first describe this theory in Sect. 1. It is sufficient for the treatment of lensing by galaxy clusters in Sect. 5, where the deflecting mass is localised in a region small compared to the distance between source and deflector, and between deflector and observer.