Gravitational Lensing from a Spacetime Perspective

Testing general relativity with cosmological large scale structure

In this paper I investigate the possibility to test Einstein's equations with observations of cosmological large scale structure. I first show that we have not tested the equations in observations concerning only the homogeneous and isotropic Universe. I then show with several examples how we can do better when considering the fluctuations of both, the energy momentum tensor and the metric. This is illustrated with galaxy number counts, intensity mapping and cosmic shear, three examples that are by no means exhaustive.

Hyperelliptic Functions and Motion in General Relativity

Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g=2: higher dimensional Schwarzschild black holes, rotating dyonic U(1)2 black holes, and black rings.

Fermat Metrics

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

Divergent reflections around the photon sphere of a black hole

From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{2 \pi }$$\end{document}e2π closer to the black hole’s optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.

Imprint of Pressure on Characteristic Dark Matter Profiles: The Case of ESO0140040

We investigate the dark matter distribution in the spiral galaxy ESO0140040, employing the most widely used density profiles: the pseudo-isothermal, exponential sphere, Burkert, Navarro-Frenk-White, Moore and Einasto profiles. We infer the model parameters and estimate the total dark matter content from the rotation curve data. For simplicity, we assume that dark matter distribution is spherically symmetric without accounting for the complex structure of the galaxy. Our predictions are compared with previous results and the fitted parameters are statistically confronted for each profile. We thus show that although one does not include the galaxy structure it is possible to account for the same dynamics assuming that dark matter provides a non-zero pressure in the Newtonian approximation. In this respect, we solve the hydrostatic equilibrium equation and construct the dark matter pressure as a function for each profile. Consequently, we discuss the dark matter equation of state and calculate the speed of sound in dark matter. Furthermore, we interpret our results in view of our approach and we discuss the role of the refractive index as an observational signature to discriminate between our approach and the standard one.

Caustics in Gravitational Lensing by Mixed Binary Systems

We investigated binary lenses with 1/rn potentials in the asymmetric case with two lenses with different indexes n and m. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different power laws to lensing by wormholes or exotic matter. In this paper, we present a complete atlas of critical curves and caustics for mixed binaries, starting from the equal-strength case, and then exploring unequal-strength systems. We also calculate the transitions between all different topology regimes. Finally we find some useful analytic approximations for the wide binary case and for the extreme unequal-strength case.

Spontaneously Scalarized Kerr Black Holes in Extended Scalar-Tensor-Gauss-Bonnet Gravity

We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.

Deflection Angle of Photons through Dark Matter by Black Holes and Wormholes Using Gauss–Bonnet Theorem

In this research, we used the Gibbons–Werner method (Gauss–Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of weak gravitational lensing within the Maxwell’s fish eye-like profile and dark-matter medium. The angle is seen as a partially topological effect, and the Gibbons–Werner method can be used on any asymptotically flat Riemannian optical geometry of compact objects in a dark-matter medium.

Metric Independence of Vacuum and Force-Free Electromagnetic Fields

Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well known to also be solutions in all spacetimes with conformally related metrics. This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry. We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field. This is demonstrated by finding a much larger class of metric transformations-involving five free functions-which preserve Maxwell solutions both in vacuum, without local currents, and also for the force-free electrodynamics associated with a tenuous plasma. One consequence of this is that many of the exact force-free fields which have previously been found around Schwarzschild and Kerr black holes are also solutions in appropriately identified flat backgrounds. As a more direct application, we use our metric transformations to write down a large class of electromagnetic waves which remain unchanged by a large class of gravitational waves propagating "in the same direction."