1,721,164 research outputs found
Optical caustics of Kerr spacetime: The full structure
No full textI present an exhaustive numerical investigation of the optical caustics in gravitational lensing by a spinning black hole for an observer at infinity. Besides the primary caustic, I examine higher order caustics, formed by photons performing one or several loops around the black hole. My investigation covers the whole parameter space, including the black hole spin, its inclination with respect to the line of sight, the source distance, and the caustic order. By comparing my results with the available analytical approximations, I find perfect agreement in their respective domains of validity. I then prove that all caustics maintain their shape (a tube with astroidal cross section) in the entire parameter space without suffering any transitions to different caustic shapes. For nearly extremal spin, however, higher order caustics grow so large that their cross sections at fixed radii wind several times around the black hole. As a consequence, for each caustic order, the number of images ranges from 2 to 2(n + 1), where n is the number of loops spanned by the caustic. As for the critical curves, I note that for high values of the spin they develop a small dip on the side corresponding to prograde orbits
Gravitational lensing in the strong field limit
No full textWe provide an analytic method to discriminate among different types of black holes on the grounds of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighborhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild, Reissner-Nordstrom, and Janis-Newman-Winicour black holes. We then compare the coefficients characterizing these metrics and find that different collapsed objects are characterized by different strong field limits. The strong field limit coefficients are directly connected to the observables, such as the position and the magnification of the relativistic images. As a concrete example, we consider the black hole at the center of our galaxy and estimate the optical resolution needed to investigate its strong field behavior through its relativistic images
Secondary caustics in close multiple lenses
No full textWe investigate the caustic structure of a lens composed by a discrete number of point-masses, having mutual distances smaller than the Einstein radius of the total mass of the system. Along with the main critical curve, it is known that the lens map is characterized by secondary critical curves producing small caustics far from the lens system. By exploiting perturbative methods, we derive the number, the position, the shape, the cusps and the area of these caustics for an arbitrary number of close multiple lenses. Very interesting geometries are created in some particular cases. Finally we review the binary lens case where our formulae assume a simple form
Gravitational lensing by black holes
No full textWe review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole
A general solution for scalar perturbations in bouncing cosmologies
No full textBouncing cosmologies, suggested by string/M-theory, may provide an alternative to standard inflation for accounting for the origin of inhomogeneities in our universe. The fundamental question is as regards the correct way to evolve the scalar perturbations through the bounce. In this work, we determine the evolution of perturbations and the final spectrum for an arbitrary (spatially flat) bouncing cosmology, the only assumption being that the bounce is governed by a single physical scale. In particular, we find that the spectrum of the pre-bounce growing mode of the Bardeen potential (which is scale invariant in some limit, and thus compatible with observations) survives unaltered in the post-bounce only if the comoving pressure perturbation is directly proportional to the Bardeen potential rather than its Laplacian, as for any known form of ordinary matter. If some new physics acting at the bounce justifies such a relation, then we are entitled to consider bouncing cosmologies as a real viable alternative for the generation of the observed inhomogeneities. Our treatment also includes some class of models with extra dimensions, whereas we show that bounces induced by positive spatial curvature are structurally different from all bounces in spatially flat universes, requiring a distinct analysis. © 2006 IOP Publishing Ltd
Caustics in special multiple lenses
No full textDespite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the others with respect to their Einstein radii, and a system where mutual distances between lenses are small compared to the Einstein radius of the total mass. Finally we review the case of a planetary system adding some new information (area of caustics, duality and higher order terms)
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