arXiv subjects

Thomas P. Kling

Publications and source records attributed to Thomas P. Kling.

16 recordsLinked to original sources

arXiv2025

Spacetime Perspective of Gravitational Lensing in Perturbed Cosmologies

We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral expressions which are used to examine the formation of multiple images and the observed shapes of non-point sources. We develop the lens mapping from the spacetime perspective, and use the Jacobian of the mapping to explain the observed image shapes. Approaching the geodesic equations as ordinary differential equations, we demonstrate the development of wave front singularities and time delays between light ray signals. This work demonstrates that the widely used thin lens approximation can be replaced with more robust techniques aligned with general relativity.

gr-qc↗

arXiv2020

Wave Fronts in a Causality Violating Godel-Type Metric

The light-rays and wave fronts in a flat class of Godel-type metric are examined to reveal the causality violating features of the space-time. Non-causal features demonstrated by the development of unusual wave front singularities are shown to be related to the non-monotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

gr-qc↗

arXiv2016

Angular diameter distances reconsidered in the Newman and Penrose formalism

Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.

gr-qc↗

arXiv2011

Accuracy of the thin-lens approximation in strong lensing by smoothly truncated dark matter haloes

The accuracy of mass estimates by gravitational lensing using the thin-lens approximation applied to Navarro-Frenk-White mass models with a soft truncation mechanism recently proposed by Baltz, Marshall and Oguri is studied. The gravitational lens scenario considered is the case of the inference of lens mass from the observation of Einstein rings (strong lensing). It is found that the mass error incurred by the simplifying assumption of thin lenses is below 0.5%. As a byproduct, the optimal tidal radius of the soft truncation mechanism is found to be at most 10 times the virial radius of the mass model.

astro-ph.CO↗

arXiv2011

Continuous image distortion by astrophysical thick lenses

Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the commonly assumed thin-lens approximation. We find that for truncated singular isothermal sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens approximation is accurate to better than 1 part in 10^4 in predicting the image area and axes ratios. For asymmetric thick lenses consisting of two massive clusters separated along the line of sight in redshift up to Δz = 0.2, we find that modeling the image distortion as two clusters in a single lens plane does not produce relative errors in image area or axes ratio more than 0.5%

gr-qc↗

arXiv2008

Poisson equation for weak gravitational lensing

Using the Newman and Penrose spin coefficient (NP) formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system.

gr-qc↗

arXiv2007

Study of errors in strong gravitational lensing

We examine the accuracy of strong gravitational lensing determinations of the mass of galaxy clusters by comparing the conventional approach with the numerical integration of the fully relativistic null geodesic equations in the case of weak gravitational perturbations on Robertson-Walker metrics. In particular, we study spherically-symmetric, three-dimensional singular isothermal sphere models and the three-dimensional matter distribution of Navarro et al. (1997), which are both commonly used in gravitational lensing studies. In both cases we study two different methods for mass-density truncation along the line of sight: hard truncation and conventional (no truncation). We find that the relative error introduced in the total mass by the thin lens approximation alone is less than 0.3% in the singular isothermal sphere model, and less than 2% in the model of Navarro et al. (1997). The removal of hard truncation introduces an additional error of the same order of magnitude in the best case, and up to an order of magnitude larger in the worst case studied. Our results ensure that the future generation of precision cosmology experiments based on lensing studies will not require the removal of the thin-lens assumption, but they may require a careful handling of truncation.

astro-ph↗

arXiv2005

The Bianchi identity and weak gravitational lensing

We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing. Using the spin coefficient formalism of Newman and Penrose [1962], we show that certain complex components of the Weyl and Ricci curvature tensors are directly related to fundamental observables in weak gravitational lensing. In the case of weak gravitational fields, we then show that the Bianchi identity provides a field equation for the Ricci tensor assuming a known Weyl tensor. From the Bianchi identity, we derive the integral equation for weak lensing presented by Miralda-Escude [1996], thus making the Bianchi identity a first principles equation of weak gravitational lensing. This equation is integrated in the important case of an axially symmetric lens and explicitly demonstrated in the case of a point lens and a SIS model.

gr-qc↗

arXiv2005

Wide-field weak lensing by RXJ1347-1145

We present an analysis of weak lensing observations for RXJ1347-1145 over a 43' X 43' field taken in B and R filters on the Blanco 4m telescope at CTIO. RXJ1347-1145 is a massive cluster at redshift z=0.45. Using a population of galaxies with 20<R<26, we detect a weak lensing signal at the p<0.0005 level, finding best-fit parameters of σ_v=1400^{+130}_{-140} km s^{-1} for a singular isothermal sphere model and r_{200} = 3.5^{+0.8}_{-0.2} Mpc with c = 15^{+64}_{-10} for a NFW model in an Ω_m = 0.3, Ω_Λ= 0.7 cosmology. In addition, a mass to light ratio M/L_R =90 \pm 20 M_\odot / L_{R\odot} was determined. These values are consistent with the previous weak lensing study of RXJ1347--1145 by Fischer and Tyson, 1997, giving strong evidence that systemic bias was not introduced by the relatively small field of view in that study. Our best-fit parameter values are also consistent with recent X-ray studies by Allen et al, 2002 and Ettori et al, 2001, but are not consistent with recent optical velocity dispersion measurements by Cohen and Kneib, 2002.

astro-ph↗

arXiv2002

Fermat Potentials for Non-Perturbative Gravitational Lensing

The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which relates the placement and distortion of the images to the real source position in the thin-lens scenario, is obtained by extremizing the time of arrival among all the null paths from the source to the observer (Fermat's principle). We show that the construction of envelopes of certain families of null surfaces consitutes an alternative variational principle or version of Fermat's principle that leads naturally to a lens equation in a generic spacetime with any given metric. We illustrate the construction by deriving the lens equation for static asymptotically flat thin lens spacetimes. As an application of the approach, we find the bending angle for moving thin lenses in terms of the bending angle for the same deflector at rest. Finally we apply this construction to cosmological spacetimes (FRW) by using the fact they are all conformally related to Minkowski space.

gr-qc↗

arXiv2000

Image distortion in non perturbative gravitational lensing

We introduce the idea of {\it shape parameters} to describe the shape of the pencil of rays connecting an observer with a source lying on his past lightcone. On the basis of these shape parameters, we discuss a setting of image distortion in a generic (exact) spacetime, in the form of three {\it distortion parameters}. The fundamental tool in our discussion is the use of geodesic deviation fields along a null geodesic to study how source shapes are propagated and distorted on the path to an observer. We illustrate this non-perturbative treatment of image distortion in the case of lensing by a Schwarzschild black hole. We conclude by showing that there is a non-perturbative generalization of the use of Fermat's principle in lensing in the thin-lens approximation.

gr-qc↗

arXiv2000

Image distortion from optical scalars in non perturbative gravitational lensing

In a previous article concerning image distortion in non-perturbative gravitational lensing theory we described how to introduce shape and distortion parameters for small sources. We also showed how they could be expressed in terms of the scalar products of the geodesic deviation vectors of the source's pencil of rays in the past lightcone of an observer. In the present work we give an alternative approach to the description of the shape and distortion parameters and their evolution along the null geodesic from the source to the observer, but now in terms of the optical scalars (the convergence and shear of null vector field of the observer's lightcone) and the associated optical equations, which relate the optical scalars to the curvature of the spacetime.

gr-qc↗

arXiv2000

Comparative Studies of Lensing Methods

Predictions of the standard thin lens approximation and a new iterative approach to gravitational lensing are compared with an ``exact'' approach in simple test cases involving one or two lenses. We show that the thin lens and iterative approaches are remarkably accurate in predicting time delays, source positions and image magnifications for a single monopole lens and combinations of two monopole lenses. In the cases studied, the iterative method provided greater accuracy than the thin lens method. We also study the accuracy of a ``2 lens, single lens plane model,'' where two monopole lenses colinear with the observer are modeled by a mass distribution in a single lens plane lying between them. We see that this model can lead to large inaccuracies in physically meaningful situations. A previous version of this paper was published as Phys.Rev.D62, 024025, (2000) with errors in the computation of two lens comparisons. This paper corrects these errors and presents new conclusions which differ from the previous version.

gr-qc↗

arXiv2000

Spacetime perspective of Schwarzschild lensing

We propose a definition of an exact lens equation without reference to a background spacetime, and construct the exact lens equation explicitly in the case of Schwarzschild spacetime. For the Schwarzschild case, we give exact expressions for the angular-diameter distance to the sources as well as for the magnification factor and time of arrival of the images. We compare the exact lens equation with the standard lens equation, derived under the thin-lens-weak-field assumption (where the light rays are geodesics of the background with sharp bending in the lens plane, and the gravitational field is weak), and verify the fact that the standard weak-field thin-lens equation is inadequate at small impact parameter. We show that the second-order correction to the weak-field thin-lens equation is inaccurate as well. Finally, we compare the exact lens equation with the recently proposed strong-field thin-lens equation, obtained under the assumption of straight paths but without the small angle approximation, i.e., with allowed large bending angles. We show that the strong-field thin-lens equation is remarkably accurate, even for lightrays that take several turns around the lens before reaching the observer.

gr-qc↗

arXiv2000

Iterative Approach to Gravitational Lensing Theory

We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.

gr-qc↗

arXiv1998

Null Cones in Schwarzschild Geometry

Light cones of Schwarzschild geometry are studied in connection to the Null Surface Formulation and gravitational lensing. The paper studies the light cone cut function's singularity structure, gives exact gravitational lensing equations, and shows that the "pseudo-Minkowski" coordinates are well defined within the model considered.

gr-qc↗