### Conveners

#### Gravitational Lensing and Shadows: Block 1

- Oleg Tsupko (Space Research Institute of Russian Academy of Sciences)
- Volker Perlick (ZARM, University of Bremen)

#### Gravitational Lensing and Shadows: Block 2

- Oleg Tsupko (Space Research Institute of Russian Academy of Sciences)
- Volker Perlick ()

#### Gravitational Lensing and Shadows: Block 3

- Oleg Tsupko (Space Research Institute of Russian Academy of Sciences)
- Volker Perlick ()

### Description

This session is devoted to gravitational lensing and shadows. Emphasis is expected to be on analytical and numerical studies. In particular, we will discuss the shadows of black holes and other compact objects, higher-order images produced by lensing and the influence of a plasma on lensing effects. Talks on other aspects of light propagation in gravitational fields are welcome as well.

The planet-size network of millimeter antennas Event Horizon Telescope (EHT) has recently delivered images of the surroundings of the supermassive compact object M87* at the center of the galaxy Messier 87. Such images are crucial to better understand the physics at play in a strong gravitational field environment. They might also allow to probe the extreme relativistic effects on the...

We study the shadow cast by rotating black holes surrounded by plasma in the context of the novel 4D Einstein-Gauss-Bonnet theory of gravity. The metric for these black holes results from applying the Newman-Janis algorithm to a spherically symmetric solution. We obtain the contour of the shadow for a plasma frequency model that allows a separable Hamilton-Jacobi equation. We introduce three...

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black...

We consider the following question: may two different black holes (BHs) cast exactly the same shadow? In spherical symmetry, we show the necessary and sufficient condition for a static BH to be shadow-degenerate with Schwarzschild is that the dominant photonsphere of both has the same impact parameter, when corrected for the (potentially) different redshift of comparable observers in the...

I will present our imaging study of four-dimensional, string-theoretical, horizonless "fuzzball" geometries. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon....

The Schwarzschild spacetime of positive mass is well-known to possess a unique “photon sphere” – meaning a cylindrical, timelike hypersurface $P$ such that any null geodesic initially tangent to $P$ remains tangent to $P$ – in all dimensions. We will show that it also possesses a rich family of spatially spherically symmetric “photon surfaces” – general timelike hypersurfaces $P$ such that any...

Consider, in the domain of wormhole, a point $p$ (observation event) and a timelike curve $\gamma$ (worldline of light source).

We prove that for infinitely many positive integers $\kappa$ there is a past-pointing lightlike geodesic $\lambda_{\kappa}$ of Morse index $\kappa$ from $p$ to $\gamma$ , hence an observer at $p$ sees infinitely many images of $\gamma$.

We will show that in the...

Current astrophysical observations show that on large scale the Universe is electrically neutral. However, locally this may be quite different. Black holes enveloped by a plasma in the presence of a strong magnetic field may have acquired a significant electric charge. We can also expect that some of these charged black holes are moving. Consequently to describe them we need spacetime metrics...

Photons emitted by light sources in the neighbourhood of a black hole can wind several times around it before fleeing towards the observer. For spherically symmetric black holes, two infinite sequences of images are created for any given source, asymptotically approaching the shadow border with decreasing magnitude. These sequences are reflected by a characteristic staircase structure in the...

Geometric optics and its corrections are typically derived using a high-frequency WKB ansatz, which results in a tower of transport equations along null geodesics. Separately, field propagation can be described using Green functions, which are known to have a Hadamard form involving certain bitensors. In this talk, it will be explained how these two perspectives on field propagation complement...

After more than a century of modern cosmology in which model assumptions were indispensable to interpret the sparse and vague data, we are finally able to replace model assumptions by observational evidence. With telescopes like Hubble, the development of adaptive optics for ground-based facilities, and installations of integrated field units, the amount of high-quality data has vastly...

Each and every observational information we obtain from the sky regarding the brightnesses, distances or image distortions resides on the deviation of a null geodesic bundle. In this talk, we will present the symplectic evolution of it on a reduced phase space. The resulting formalism is analogous to the one in paraxial Newtonian optics. It allows one to identify any spacetime as an optical...

I will discuss a new method of determining the spacetime curvature and matter density along the line of sight using variations of times of arrival (TOA) of electromagnetic signals, measured in the vicinity of two given points. We measure the variations of the TOA's up to quadratic order in the displacements of the source and the receiver with the help two groups of synchronised clocks,...

We investigate the rotation of the polarization of a light ray propagating in the gravitational field of a circularly polarized laser beam. The rotation consists of a reciprocal part due to gravitational optical activity, and a non-reciprocal part due to the gravitational Faraday effect. We discuss how to distinguish the two effects: letting light propagate back and forth between two mirrors,...

The maximal analytic extension of slow Kerr spacetime contains an infinity of asymptotically flat ”exterior” regions connected by a strongly curved region. General relativistic ray tracing is used to calculate videos showing the view of an observer moving through Kerr spacetime. Covering the whole maximal analytic extension requires a multitude of coordinate patches. The calculated videos give...

It is now clear beyond any doubt that neutrinos have masses, and that they mix. Experiments with solar, atmospheric, reactor and accelerator neutrinos have determined, with remarkable accuracy, values of $\Delta m_{ij}^2 = m_i^2 -m_j^2 $. Absolute neutrino masses, however, are still unknown. We know neutrino vacuum oscillations only depend on $\Delta m^2$, hence, oscillations experiments are...

**What do archival observations tell us about the M87 black hole?**

With the 2017 observations of the Event Horizon Telescope we observed the M87 supermassive black hole with linear resolution corresponding to about 3 Schwarzschild radii, revealing a bright ring surrounding dark center – a feature dubbed a “black hole shadow”. Several archival observations of M87 with the EHT prototype...

Gravitational lensing is a widely used probe in the study of the dark universe. Besides the gravity, the free electrons in the plasma can also cause deflections of the light. Although plasma lensing has a distinct similarity to gravitational lensing, particularly in its mathematical description, plasma lensing introduces additional features, such as wavelength dependence, diverging deflection,...

In spherically symmetric and static spacetimes, gravitational

lensing can be formulated in terms of an exact lens map, in

close analogy to the weak-field formalism of lensing. Whereas

in the latter case the lens map is a map from a lens plane to

a source plane, the exact lens map is a map from the celestial

sphere of the observer to a sphere where the light sources are

thought to be...

We investigate strong-field gravitational lensing by rotating Simpson-Visser black hole, which has an additional parameter ($l$), apart from mass ($M$) and rotation parameter ($a$). It can admit Cauchy and event horizons for some parameters and free from the singularity and assess phenomenological differences from the Kerr black holes. We also find a decrease in the deflection angle...

A photon region in the black holes gravitational field is defined as a compact region where photons can travel endlessly without going to infinity or disappearing at the event horizon. In the Schwarzschild metric, the photon region degenerates to the photon sphere which is a three-dimensional umbilic hypersurface in spacetime (its second quadratic form is proportional to the induced metric)....

We present a purely geometric method for constructing a rank two Killing tensor in a spacetime with a codimension one foliation that lifts the trivial Killing tensors from slices to the entire manifold [1]. The resulting Killing tensor can be nontrivial. A deep connection is found between the existence of such a Killing tensor and the presence of generalized photon surfaces in spacetime with...

We present a unified formulation of geometrical optics in General Relativity. Consider two causally connected, locally flat neighborhoods. Suppose that each null geodesic originating in one neighborhood terminates at the other one, and the curvature along the trajectory is small enough, such that the linear geodesic deviation equation holds. Also, let the observation be performed by a number...

A black hole's shadow is expected to deform under the influence of an external gravitational field caused by matter present in its vicinity. This talk aims to characterise the distortion of a Schwarzschild black hole shadow due to a non-zero quadrupole moment $c_2$ by qualitatively investigating the behaviour of light rays close to the black hole horizon. In particular, the numerical...

Advancements in the black hole shadow observations may allow us not only to investigate physics in the strong gravity regime, but also to use them in cosmological studies. We propose to use the shadow of supermassive black holes as a standard ruler for cosmological applications assuming the black hole mass can be determined independently. First, observations at low redshift distances can be...