Short review of the Weyl geometry is given. To describe the phenomenological particle creation we suggest the modified perfect fluid model taking into account the back reaction on the geometry of both the already created particles and the very process of their creation. It is found that the relation for particle creation is conformal invariant. This requires the creation law consisting of the source terms as the Weyl Lagrangian plus two quite new terms depending of the particle number density.

We generalize the notion of Einstein-Rosen bridge by defining it as a space-like connection between two universes with regions of asymptotically minkowskian space-time infinities.The corresponding symmetry and asymmetry properties of the generalized Einstein-Rosen bridge are considered at the cases of Reissner-Nordstr öm and Kerr metrics.We elucidate the versatility of intriguing symmetry and asymmetry phenomena outside and inside black holes.For description of the test particle (planet and photon) motion it is used the Kerr-Newman metric of the rotating and electrically charged black hole.In particular, it is demonstrated the symmetry and asymmetry of the one-way Einstein-Rosen bridge inside black hole toward and through the plethora of endless and infinite universes.

We describe the possible forms of black hole images viewed by a distant observer (or a telescope) on the celestial sphere. These images are numerically calculated based on general relativity and the equations of motion in the Kerr–Newman metric. A black hole image is a gravitationally lensed image of the black hole event horizon. It may be viewed as a black spot on the celestial sphere, projected inside the position of a classical black hole shadow. In the nearest future it will be possible to verify modified gravity theories by observations of astrophysical black holes with Space Observatory Millimetron.

We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the Universe 'from nothing' in the vacuum state, we investigated the problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for dark matter.

Памяти Вениамина Сергеевича Березинского, Агафонова Н.Ю., Газизов А.З., Докучаев В.И., Долгов А.Д., Домогацкий Г.В., Ерошенко Ю.Н., Либанов М.В., Матвеев В.А., Постнов К.А., Птускин В.С., Рубцов Г.И., Смирнов А.Ю.

A short introduction to Weyl geometry and Weyl gravity is given. The self-consistency relation for the variation of the general form of the matter action integral to be conformal invariant is obtained. It is shown that the particle production rate per unit coordinate volume per unit coordinate time is conformal invariant. It is noticed that such a feature allows us to consider the perfect fluid action as an example of the Sakharov™s induced gravity model.

We reconstructed dark spots in the images of supermassive black holes SgrA* and M87* provided by the Event Horizon Telescope (EHT) collaboration by using the geometrically thin accretion disk model. In this model, the black hole is highlighted by the hot accretion matter up to the very vicinity of the black hole event horizon. The existence of hot accretion matter in the vicinity of black hole event horizons is predicted by the Blandford-Znajek mechanism, which is confirmed by recent general relativistic MHD simulations in supercomputers. A dark spot in the black hole image in the described model is a gravitationally lensed image of an event horizon globe. The lensed images of event horizons are always projected at the celestial sphere inside the awaited positions of the classical black hole shadows, which are invisible in both cases of M87* and SgrA*. We used the sizes of dark spots in the images of SgrA* and M87* for inferring their spins, 0.650.75, accordingly.

We describe quantum correction to the accreting hot plasma onto black holes. The accreting black holes are surrounded by the very hot ionized plasma. This plasma is heated inevitably by the outgoing photons of the quantum Hawking radiation. It is demonstrated that Hawking radiation prevails over the Compton scattering of hot electrons in the accreting flow onto the small enough evaporating black holes.

We elucidate the versatility of intriguing symmetry and asymmetry phenomena outside and inside black holes. For description of the test particle (planet and photon) motion it is used the Kerr-Newman metric of the rotating and electrically charged black hole. In particular, it is demonstrated the symmetry and asymmetry of the one-way Einstein-Rosen bridge inside black hole toward and through the plethora of endless and infinite universes.

These are lectures for students at the summer school conducted by the Faculty of Fundamental Sciences, Bauman Moscow State Technical University at 2022.

We elucidate the physical origin of the dark spot in the image of supermassive black hole SgrA* presented very recently by the EHT collaboration. It is argued that this dark spot, which is noticeably smaller than the classical black hole shadow, is the northern hemisphere of the event horizon globe. The classical black hole shadow is unseen in the image of SgrA*. The dark spot in the image of SgrA* is projected within the position of the classical black hole shadow on the celestial sphere. The outer boundary of this dark spot is an equator on the event horizon globe.

A fast progress in the observational technologies in astrophysics provides the unique possibility for detailed observations of black holes in the nearest future. It would be possible to verify general relativity and its numerous modifications in the strong field limit by using observational data from the advanced cosmic interferometric observatories. We review the modeled images of the rotating black hole in different appropriate cases: the luminous distant background, the thin accreting disk and the luminous moving hot spots in relativistic jets along the black hole rotation axis.

The homogeneous and isotropic cosmological model in the Weyl conformal geometry is considered. We showed that, despite the conformal invariance, the dust matter is allowed in such a universe. It is shown that the number of dust particles is not conserved, i.e. they are continuously produced. The general form of the law for their creation is found.

The Dust Complex (DC) instrument was designed to be installed on the landing platform of the ExoMars project. The purpose of the experiment is to study the dynamics of dust particles in the near-surface atmosphere of Mars and to evaluate the main characteristics of the near-surface medium that determine their dynamics. The device makes it possible to register dust particles in the near-surface atmosphere of Mars, determine the main parameters and measure some characteristics of the plasma-dust medium related to the dynamics of dust particles near the Martian surface. The article provides a description of the device, its blocks and sensors, the main elements of the measurement program and characteristics of the measured parameters.

The program of scientific research of the Luna-25 lunar lander includes the experiment "Dust monitoring of the Moon" (in Russian, "Pylevoi monitoring Luny" (PmL)), which provides for the study of the dynamics of lunar microparticles and parameters of the near-surface dusty plasma. Using the PmL instrument, it is planned to record for a long time individual microparticles above the lunar surface, to measure and evaluate their physical characteristics (momentum, velocity, charge, mass, and concentration), as well as to monitor the dynamics of the parameters of the near-surface dusty plasma environment (density, temperature, and potential). The instrument has passed successfully the entire range of ground tests.

In construction of the conformal invariant Lagrangian we restrict ourselves to the so-called Quadratic Gravity. Then, in the Riemannian geometry there exist only one suitable combination, namely, the square of the Weyl tensor (completely traceless part of the curvature tensor). The corresponding left-hand side of the field equations, the Bach tensor, is linear in the Weyl tensor itself and its second covariant derivatives. But, for any homogeneous and isotropic cosmological space-time (i.e., Robertson-Walker metric with arbitrary scale factor) the Weyl tensor is identically aero. Thus, any cosmological metric is the vacuum solution of the Weyl gravity in the framework of the Riemannian geometry – no matter at all! In 1919 Hermann Weyl invented a new geometry, which is now called the Weyl geometry. He introduced some 1-form and incorporated it into the connections by demanding that the new covariant derivative of the metric tensor coefficient equals this 1-form times that very coefficient. Then, he showed that in order these new connections to be conformal invariant, the 1-form must behave under the conformal transformation of the metric as the gauge field. It was the great discovery! How about the cosmology in the Weyl geometry? We started with construction the Lagrangian for the single particle moving in the given gravitational field in the Weyl geometry and discovered that there may exist some new interaction, absent in the Riemannian geometry (and, particularly, in General Relativity). This is due to the existence of the yet another invariant, namely, the contraction of the 1-form with the particle four-velocity vector. We called it “the invariant B”. And we were able to incorporate it into the Lagrangian for the perfect fluid. The cosmological principle requires that the Weyl 1-form should have only one (temporal) non-vanishing component depending only on the time coordinate. Hence, it can be removed by a suitable conformal transformation (also depending only on time). In such a gauge all possible functions of our new invariant B are converted into the set of some constants. The corresponding solutions we called “the basic solutions”. Given the basic solutions, the general ones are obtained by the arbitrary time-depending conformal transformation of both metric tensor and the 1-form. The important role in the existence of the non-trivial cosmological solutions is played by the possibility of the particle creation. The important problem is the comparison with the observations. By doing that and extracting some consequences we are using the cosmological equations of General Relativity, namely, the Friedmann equation. But now our gravitational equations are quite different. Therefore, we must rewrite them as the Friedman equations on the right-hand-side and some effective energy-momentum tensor on the left-hand-side. Of course, such an effective energy-momentum tensor may have nothing in common with the primary one. It appears that in the rather simple non-trivial basic solution we found, the effective energy-momentum tensor contains the cosmological term absent at the beginning. The details we will be presented in the talk.

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.

We derived the equations for the double layers in quadratic gravity, using solely the least action principle. The advantage of our approach is that, in the process of calculation, the δ ′-function does not appear at all, and the δ -functions appear for a moment and are mutually canceled prior to integration. We revealed the peculiar structure of the obtained equations, namely, that the surface energy–momentum tensor of the matter fields (constituents of the thin shells) does not play a role in the determination of the trajectory of the double layer. Also, we suggested that the space-like double layers may provide us with the adequate description of the creation of the Universe from the black hole singularity. The related topics, including the Gauss–Bonnet term and F ( R )-theories, are shortly discussed.

The paper presents an acousto-optic lunar infrared spectrometer (LIS) intended for mineralogical analysis and assessment of the hydration of the lunar surface regolith near the lander. Its optical layout, characteristics, results of calibrations and laboratory measurements are given. The LIS is designed to measure the spectrum of solar radiation reflected by the lunar surface; it will function as part of the load complex of the Luna-25 lander. The instrument is mounted on the manipulator of the lander in such a way that its field of view is within the field of view of the television support stereo cameras of the robotic arm working zone (TV RPM). The instrument operates in the spectral range of 1.15–3.4 µm, including the OH/H2O absorption bands, with a spectral resolution of approximately 25 cm–1. The principle of operation of the device is based on acousto-optic spectral filtering of optical radiation.