Gravitational lens optical scalars in terms of energy-momentum distributions

Abstract

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.PACS numbers: 95.30.Sf

Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor

“…In this section we argue that because the spatial orbits of light rays in a plasma can be found by studying null geodesics in the associated 4-dimensional Gordonlike metric, it is possible to apply the null tetrad approach with a gravitational lens surrounded by plasma. The null tetrad approach was used by Gallo and Moreschi in [1] to study the bending angle and optical scalars in pure gravity.…”

“…Therefore, for the pure gravity case there are at least two alternative methods to compute the deflection angle and related optical quantities in terms of coordinate-free quantities: on the one hand the null-tetrad approach [1,31], and on the other the Gibbons-Werner method [34]. Note that even when these two methods are geometrical, the associated geometrical quantities refer to two different manifolds (a four-dimensional Lorentzian metric in the case of [1]) and a two-dimensional Riemannian metric in the case of [34]. As we mentioned above, we have also recently extended the use of the Gibbons-Werner method to more general situations where dispersive media are present.…”

“…As we mentioned above, we have also recently extended the use of the Gibbons-Werner method to more general situations where dispersive media are present. A natural question arises: can the null tetrad method developed in [1] also be extended to apply to dispersive media? It is one of our goals in this article to answer this question positively by showing that the null-tetrad approach can be extended to incorporate the influence of a plasma medium on the deflection angle and other optical quantities when static, asymptotically flat and spherically symmetric spacetimes are considered.…”

Higher order corrections to deflection angle of massive particles and light rays in plasma media for stationary spacetimes using the Gauss-Bonnet theorem

“…In [18] it was established for the first time a correspondence between the motion of light rays in a particular non-homogeneous plasma and the one of relativistic test charged massive particles in vacuum. In the same work, the Gauss-Bonnet method was applied to obtain an expression for the deflection angle in terms of the components of the energy-momentum tensor in a plasma environment generalizing in this way previous works restricted to the pure gravity case [19][20][21][22].…”

Efficient gravitational lens optical scalars calculation of black holes with angular momentum

“…It is often the case that the lens can be assumed to be thin. In those circumstances one can proveGallo & Moreschi (2011) that the optical scalars can be expressed by…”