Related papers: A Lefschetz fixed point theorem in gravitational l…
We introduce a new adaptive and fully Bayesian grid-based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark-mass substructure in massive galaxies,…
Several recent papers have suggested that the cosmological constant Lambda directly influences the gravitational deflection of light. We place this problem in a cosmological context, deriving an expression for the linear potentials which…
We discuss gravitational lensing in the Kehagias-Sfetsos space-time emerging in the framework of Ho\v{r}ava-Lifshitz gravity. In weak lensing we show that there are three regimes, depending on the value of $\bar {\lambda}=1/\omega d^{2}$,…
We present a formal derivation of the key equations governing gravitational lensing in arbitrary space-times, starting from the basic properties of Jacobi fields and their expressions in terms of the exponential map. A careful analysis of…
Topological invariants characterising filled Bloch bands attract enormous interest, underpinning electronic topological insulators and analogous artificial lattices for Bose-Einstein condensates, photons, and acoustic waves. In the latter…
In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points. The geometric model incorporates the fine arithmetic properties of the rotation number at the fixed point. Using this model for the…
In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an…
Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. We prove a "quantum Riemann-Roch…
We investigate imaging point sources with a monopole gravitational lens, such as the Solar Gravitational Lens in the geometric optics limit. We compute the light amplification of the lens used in conjunction with a telescope featuring a…
Building on a recent joint paper with Sturmfels, here we argue that the combinatorics of matroids is intimately related to the geometry and topology of toric hyperkaehler varieties. We show that just like toric varieties occupy a central…
Adopting the strong field limit approach, we investigate the strong gravitational lensing of a spherically symmetric spacetime in the Einstein-Proca theory. With the strong field limit coefficient, three observable quantities are obtained,…
We study the general theorem about gravitational lensing which states the relationship between the numbers of images with different parities. Our formulation allows an extension to the nontransparent and singular model.
Introducing the primed inertial coordinate system, for each inertial frame of reference, in addition to the usual inertial coordinate system, we assume that gravity-free space and time possess the Euclidean structures in the primed inertial…
In this work, we study the gravitational lensing by a Lorentz-violating (LV) black hole inspired by the recent contribution [1]. Explicitly, we concentrate on a specific application: we perform the computation of gravitational lensing…
Topological photonics has attracted increasing attention in recent years due to the unique opportunities it provides to manipulate light in a robust way immune to disorder and defects. Up to now, diverse photonic platforms, rich physical…
Gravitational lensing caused by the gravitational field of massive objects has been studied and acknowledged for a long period of time. In this paper, however, we propose a different mechanism where the bending of light stems from the…
We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefschetz fixed-morphism theorem. In order to do so, we use the…
Of order one in 10^3 quasars and high-redshift galaxies appears in the sky as multiple images as a result of gravitational lensing by unrelated galaxies and clusters that happen to be in the foreground. While the basic phenomenon is a…
We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the…
We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results…