International Journal of Modern Physics A

The definitions of classical and quantum singularities are reviewed. While it is known that some classical timelike and null singularities in static and conformally static spacetimes are resolved by a quantum probe, here it is shown that the ring singularity in the stationary overspinning Kerr spacetime remains singular.

The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.

Here we propose an experiment to test the exotic spin-dependent interaction that can be mediated by axion-like particles. A sensitive cantilever is used to measure the force between a Bi₄Ge₃O${}_{12}$ (BGO) microsphere and a spin-polarized magnetic structure. The magnetic structure consists of alternate reversely spin-polarized electrons. The magnetic structure is to be driven to oscillate during data acquisition, thus the exotic force signal is modulated to the high harmonics of the drive frequency. This helps to suppress the spurious background signal. The separation between the BGO sphere and the magnetic structure can be as close as 3.5 $\mu$m, and the force sensitivity is expected to be $\sim$ 1 fN. If a Null result is obtained, the constraints on the coupling constant could be four orders of magnitude stronger than the current status of the experimental test at $\lambda$ = 10 $\mu$m.

Static and stationary cylindrically symmetric space-times in general relativity are considered, supported by distributions of cosmic strings stretched in the azimuthal ($\phi$), longitudinal ($z$) or radial ($x$) directions or and by pairs of mutually opposite radiation flows in any of these directions. For such systems, exact solutions are obtained and briefly discussed, except for radial strings (a stationary solution for them is not found); it is shown that static solutions with $z$- and $\phi$-directed radiation flows do not exist while for $z$-directed strings a solution is only possible with negative energy density. Almost all solutions under discussion contain singularities, and all stationary solutions have regions with closed timelike curves, hence, most probably, only their well-behaved regions admit application to real physical situations.

We revisit Weyl’s unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of geometrization of physics started by Einstein to include the electromagnetic field, H. Weyl developed a new geometry which constitutes a kind of generalization of Riemannian geometry. However, despite its mathematical elegance and beauty, a serious objection was made by Einstein, who considered Weyl’s theory not suitable as a physical theory since it seemed to lead to the prediction of a not yet observed effect, the so-called “second clock effect”. In this paper, our aim is to discuss Weyl’s proposal anew and examine its consistency and completeness as a physical theory. Finally, we propose new directions and possible conceptual changes in the original work. We believe that in this way we could perhaps be led to a rich and interesting new modified gravity theory.

The general action functional for a scalar-tensor theory of gravitation without derivative couplings is considered together with its special case of the Brans–Dicke theory. The aim of the paper is to clarify the problem of anomalous limit of the Brans–Dicke to the Einstein gravity.

Modernized version of the combined opto-acoustical gravitational wave detector OGRAN is presented. Located in the deep underground of the Baksan Neutrino Observatory this setup is aimed to work on the program of collapsing stars searching for in multi-channel manner with the neutrino telescope BUST. The both instruments have the sensitivity allowing a registration of collapses in our Galaxy as rare events with the estimated probability $0.03$ year${}^{-}1$. The OGRAN narrow band sensitivity at the kilohertz frequency is limited by its acoustical mode thermal noise achieving $10^{-20}$ in term of metric perturbations. A possible algorithm of the joint data analysis for the both instruments is developed and resulting formulae of the right detection probability are given. A future increasing of the OGRAN sensitivity associated with the moderate cooling (nitrogen temperature) of the acoustical mode is also discussed.

Many theoretical approaches aiming to explain dark matter or dark energy predict variations of Newton’s law of gravity at sub-millimeter separations. In this low-energy domain, force metrology provides an alternative to astronomical observations and high-energy experiments in the search for new physics. The Casimir And Non-Newtonian force EXperiment (CANNEX) has been designed from the ground up to allow for metrological force measurements between truly parallel macroscopic flat plates in the separation range 3–30 micrometer. Benefiting from this geometry, the experiment could potentially reach sensitivities of $0.1$nN/m² for pressures and $1$mN/m³ for pressure gradients. Achieving such precision would enable us to test a variety of non-Newtonian interactions and to unambiguously detect thermal Casimir forces at large separation. In this paper, we review the experimental setup together with proposed improvements, and give an outlook on potential measurements that will be performed once the setup has been rebuilt at its new location in Vienna.

We show that the rotating black hole solutions bring new effects in the particle physics, allowing to unite gravity with quantum theory. Due to extremely large spin/mass ratio (for typical spinning particles), the rotating Kerr black hole solution deforms space topologically on the Compton scale, which increases extremely effective influence gravity on quantum processes, and gravity starts to collaborate with quantum processes, instead of confront them. In particular, Kerr’s gravity defines several important structures and parameters of electron, in particular, its non-perturbative shape, the associated Wilson loop, features of the used supersymmetry and specials of the stringy system.

We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically. We show that the connection can be integrated out, resulting in an equivalent metric theory. Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field. We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame. Still, as this connection enters the action algebraically, the theory admits the dynamically equivalent (pseudo)-Riemannian formulation in the form of an effective metric theory with an extra K-essence term. This may have interesting phenomenological applications.

The motion of a test null string “inside” an axially symmetric domain of null strings which has a layered structure and radially changes its size has been investigated. It is shown that the action of the gravitational field of such a domain on a test null string for any initial conditions leads to oscillations of a test null string inside a region limited in space. The motion (drift) of the region inside which the test null string oscillates depends on the ratio of the initial parameters characterizing the test null string and the null string domain. These regions can be considered as particles localized in space with an effective nonzero rest mass. For these particles, you can enter the concept of “life time”, which depends on the number of layers in the multi-string system. It is also possible to introduce the concept of particle “mass” (energy), which is determined by the size of the region in which the null string oscillates and depends on the trajectory of the null string in this region. Under the influence of changing external conditions one kind of particles can pass into another.

An updated review of Kraichnan’s derivation of Einstein’s equations from quantum field theory is presented, including the period after the discovery of the Higgs mechanism and the inclusion of gravitation within the Standard Model of Fundamental Interactions.

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrödinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $\mathrm{\Lambda }$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.

In a recent work we derived the kinematic Hamiltonian and primary constraints of the new general relativity class of teleparallel gravity theories and showed that these theories can be grouped in 9 classes, based on the presence or absence of primary constraints in their Hamiltonian. Here we demonstrate an alternative approach towards this result, by using differential forms instead of tensor components throughout the calculation. We prove that also this alternative derivation yields the same results and show how they are related to each other.

This work is devoted to exploring the stability of thin-shell wormholes developed from two equivalent copies of charged quintessence (charged Kiselev) black holes by using Visser cut and paste approach. The characteristics of the surface matter of the shell are determined by using Israel formalism. We examine the stability of thin-shell by assuming a barotropic equation of state for the surface matter of the wormhole throat. We conclude that wormhole becomes stable in the presence of both charge and Kiselev parameter otherwise, it shows an unstable behavior.

We consider a relation between the Huygens Principle (HP) in gravity and the self-interaction force. We show that the self-force for an electric particle in the plane gravitational wave space-time has no tail term even the vector Green function does not obey the HP. The reason for this observation is that even vector potential does not obey the HP, the electromagnetic field does obey.

We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of Schrödinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the “active” gravitational masses are always positive, and approximately equal to inertial masses and to the mass $m$ of the quanta of Dirac field up to the corrections of order ${\alpha }^2$. Here $\alpha ={(m/M_{pl})}^2$ is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit $\alpha =0$ the model reduces back to the nonrelativistic Schrödinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is $\alpha$ times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process.

We explore the interplay between quantization, local commutativity and the analyticity properties of the two-point functions of a quantum field in a non trivial topological cosmological background in the example of the two-dimensional de Sitter manifold and its double covering. The global topological differences make the many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum and there are no $SL(2,R)$-invariant fields whose mass is less than 1/2.

Vacuum solutions describing thick branes with codimension 1 within higher-dimensional $f(R)=-\alpha R^n$ modified gravity are constructed. The dependence of these solutions on the parameters determining the solutions is studied numerically.

Using the observational properties of Einstein’s gravitational field it is shown that a minimum of four non-coplanar mass probes are necessary for a Michelson and Morley interferometer to detect gravitational waves within the context of General Relativity. With fewer probes, some alternative theories of gravitation can also explain the observations. The conversion of the existing gravitational wave detectors to four probes is also suggested.

The concept of unified field theory is discussed. Two nonlinear field models with world volume type action are considered, namely extremal space-time film model and Born–Infeld nonlinear electrodynamics. The natural appearance of two long-range fundamental interactions, electromagnetism and gravitation, in these field models is discussed. The quantum behavior of the interacting solitons-particles is considered. The concept of quasi-bounding quantization in nonlinear field models is introduced.

The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$ gravity, which is the pseudo-invariance of $T$ under a local symmetry, to understand the nature of the extra d.o.f.

The global time in geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The reduced Hamiltonian equations of motion of gravitational field in semi-geodesic coordinate system are written.

We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the $k$-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius $r_e=9.2\sqrt{\alpha /4\pi }\sqrt{\hslash G/c^3}=9.2\sqrt{\alpha /4\pi }{l}_P\approx 10^{-36}$m, where ${\ell }_P=\sqrt{\hslash G/c^3}$ is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at $(8/3)\sqrt{\alpha /4\pi }\sqrt{\hslash c/G}=(8/3)\sqrt{\alpha /4\pi }{m}_P=10^{17}$ GeV in terms of the Planck mass $m_P$. The unified field depends on $e$ and $G$ alone, independent of $\hslash$; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at $r_e$.

We consider the classical bremsstrahlung of an ultrarelativistic point-like particle on potential, generated by the free infinite Nambu-Goto object ($p$-brane). For simplicity, the interaction is supposed to take place via the bulk scalar field. Scalar interaction can model both the vector field and the trace part of linearized gravity. The particle does not intersect the Nambu-Goto object and moves in transverse directions, thus in the ultrarelativistic limit we can regard its trajectory as straight and make use of the perturbation theory. We derive the radiation amplitudes and compute the emitted energy during the collision. The validity of classical consideration is discussed. The results are analyzed in the context of co-dimensionality of the brane embedding.

We show that the scattering of radiation on a traversable wormhole forms a vortex in the radiation energy flux. Then, if the wormhole possesses also a magnetic fields, the vortex accelerates charged particles along the magnetic lines and such a system works as an accelerator. If the vortex is small, the system reaches the stationary state, when the income of the kinetic energy reradiates completely in the form of the synchrotron radiation. Such a mechanism allows us to relate a part of observed sources of the synchrotron radiation to magnetic wormholes.

We recall the motivation for an external scalar field, $\psi$, and show how it helps to improve the 5D Kaluza-Klein theory. Various applications of the theory that fit observational or experimental data in the laboratory as well as in the cosmological or astrophysical contexts are mentioned. Special attention is given to the last version of the experiment showing evidence of a torque on a torsion pendulum as predicted by the theory. New arguments that motivate extradimensions are put forward.

At the present moment, there is an unresolved problem in the physics of cosmic rays. The problem concerns the origin of the ultrahigh energy cosmic rays. One of the possible mechanisms of the particle’s birth with such energy is bound to the processes occurring in the active nuclei of the galaxies. In this paper, we have examined a collision of superheavy particles. Using the Weinberg formalism, we have estimated gravitational radiation emitted during the collision in the first approximation. It was shown that, for a certain collision time, the energy lost by the ultrarelativistic particle is less than the value of the energy of the mass center of the collision and the mass of the colliding particles.

We investigate the vacuum expectation value of the energy-momentum tensor and the Casimir forces for the electromagnetic field in AdS spacetime for the geometry of two parallel plates. On the plates the field obeys the boundary condition that generalizes the perfect conductor boundary condition for an arbitrary number of spatial dimensions. The interaction forces between the plates are attractive. At separations larger than the curvature radius of the spacetime they decay exponentially.

We consider the gravity-induced effects associated with a massless scalar field living in a higher-dimensional spacetime being the tensor product of Minkowski space and spherically-symmetric space with angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole or cosmic string with flat extra dimensions, where the deficit of solid angle is proportional to Newton constant and tension. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green’s function and compute it to the leading order. With the use of this Green’s function we compute the renormalized vacuum expectation value of the scalar-field’s energy-momentum tensor. We make some general note on the linear-on-curvature part of the trace of even coefficients of Schwinger-deWitt expansion.

We perform quantization of a model in which gravity is coupled to a circular dust shell in $2+1$ spacetime dimensions. Canonical analysis shows that momentum space of this model is $AD{S}^2$-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.

Using the logarithmic superfluid model of physical vacuum, one can formulate an essentially quantum post-relativistic theory, which successfully recovers Einstein’s theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We present an analytical example of the dispersion relation and show that it should have a Landau form which ensures the suppression of dissipative fluctuations. We show that in the low-momentum sector of the theory, a dispersion relation becomes relativistic with small deformations, such that a photon acquires effective mass, but a much more complex picture arises at large momenta.

In this paper we give necessary transformation to diagonalize generalized Vaidya spacetime in the simplest cases.

The problem of particle creation in cosmology concerning whether the results for the number of particles are infinite or finite is discussed for scalar and spinor particles in Friedmann expanding Universe. It is shown that the results are always finite if one puts in case of scalar particles creation a special term into the Lagrangian. Numerical estimates of the effect of particle creation are made. The role of creation of superheavy particles in cosmology is discussed.

We point out that gravitational wave detectors such as LISA have the potential of probing a cosmological time evolution of the Higgs boson self-coupling constant $\lambda$ and thus the Higgs boson’s mass $m_H=\sqrt{2\lambda }v$. The phase transition of the Standard Model could have been a first order one if the Higgs mass was below 72 GeV at a temperature $T_{\star }\ge 100$ GeV. Gravitational waves could thus have been produced during the electroweak phase transition. A discovery by LISA of a stochastic background of gravitational waves with a characteristic frequency $k_{\star }\ge 10^{-5}$ Hz could be interpreted as a sign that the Higgs boson self-coupling constant was smaller in the past. This interpretation would be particularly tempting if the Large Hadron Collider did not discover any physics beyond the Standard Model by the time such waves are seen. The same mechanism could also account for baryogenesis.

In connection with the problem of dark matter, we discuss recent results on constraining the parameters of axion-to-nucleon interaction following from the experiment on measuring the difference of Casimir forces. It is shown that this experiment not only leads to competitive constraints, but provides stronger support to other constraints obtained in Casimir physics so far. The description of dark energy by means of cosmological constant originated from the quantum vacuum is considered in terms of the renormalization procedures in quantum field theory. It is argued that only the renormalized value of cosmological constant directly connected with the observed density of dark energy is of physical significance, so that some statements in the literature concerning the vacuum catastrophe may be considered as an exaggeration.

We present a special case of the Stephani solution with spherical symmetry while considering different values of spatial curvature. We investigate the dynamics of the universe evolution in our model, build the R–T-regions for the resulting spacetime and analyze the behavior of the deceleration parameter. The singularities of the model are also discussed. The geometry of the spatial part of the obtained solution is explored.

The Dark Side of the Universe, which includes the cosmological inflation in the early Universe, the current dark energy and dark matter, can be theoretically described by supergravity, though it is non-trivial. We recall the arguments pro and contra supersymmetry and supergravity, and define the viable supergravity models describing the Dark Side of the Universe in agreement with all current observations. Our approach to inflation is based on the Starobinsky model, the dark energy is identified with the positive cosmological constant (de Sitter vacuum), and the dark matter particle is given by the lightest superparticle identified with the supermassive gravitino. The key role is played by spontaneous supersymmetry breaking.

We discuss a proposal for a somewhat new formulation of quantum field theory (set in a four-dimensional manifold, the space-time) that includes an analysis of its implications for the evolution of Einstein-Friedmann cosmological models. The proposed theory displays two peculiar features: (i) a local Hilbert-Fock space is associated with each space-time point: we are dealing with a vector bundle whose fibers are Hilbert spaces; the operator-valued sections of the bundle are the quantum fields; (ii) the vacuum energy density is finite, being regularized in a space-time curvature dependent way, independently at each point. In fact everything is finite: self-masses, self-charges, quantum fluctuations: they depend on the space-time curvature and diverge only for a flat metric. In an Einstein-Friedmann model the vacuum (zero-point) energy density is consequently time-dependent and in general not negligible. Then it is shown that, for some choices of the parameters of the theory, the big-bang singularity is resolved and replaced by a bounce driven by the vacuum energy density, which becomes (very) large and negative near the bounce (negative by the contribution of the Fermi fields). But for large times (now, say) the Bose fields’ positive vacuum energy eventually overcomes the negative one and we are finally left with the present vacuum energy: positive and reasonably small.

The conditional principle of extremum in quantum cosmology is formulated for a positive functional of the energy density of space, in which gravitational constraints serve as additional conditions. The extremum conditions determine the discrete spectrum of the “stationary” state of the universe with the corresponding values of the energy density of space. A dynamic interpretation of solutions is proposed, in which the quantum number of the energy density plays the role of cosmic time. In the self-consistent harmonic approximation, the quantum dynamics of the anisotropic model of the Bianchi IX universe is considered.

Viscous properties are attributed to the dark sector of the Universe. They contribute to the accelerated expansion phase of the Universe and can alleviate existing tensions in the $\mathrm{\Lambda }$CDM model at small scales. We provide a short review of recent efforts on this topic. Different viscous models for the dark sector are analysed both from theoretical and observational point of view.

An anisotropic cosmological model with expansion and rotation and the Bianchi type IX metric has been constructed within the framework of general relativity theory. The first inflation stage of the Universe filled with a scalar field and an anisotropic fluid is considered. The model describes the Friedman stage of cosmological evolution with subsequent transition to accelerated exponential expansion observed in the present epoch. The model has two rotating fluids: the anisotropic fluid and dust-like fluid. In the approach realized in the model, the anisotropic fluid describes the rotating dark energy.

In this work, we study the effects of Generalized Uncertainty Principle on the evolution of the Universe through Friedmann’s equations. We show that the effects are equivalent to those of the cosmological constant and thus they constitute an additional contribution in the acceleration of the expansion of the Universe.

It is shown that in the rest frame of the observer in expanding Universe states of particles with negative energy exist.The properties of such states are studied. The comparison with the case of negative energies of particles in black holes and rotating coordinates out of the static limit is made.

We investigate the cosmological dynamics of nonlocally corrected gravity involving a function of the inverse d’Alembertian acting on the Gauss-Bonnet term. Casting the dynamical equations in local form, we derive the reconstruction procedure. We find conditions on the model parameters that are sufficient for the existence of de Sitter solutions and obtain these solutions explicitly.

The accumulation of dark matter particles near the primordial black holes starts at the radiation-dominated cosmological stage and produces the central density spikes. The spikes can be the bright gamma-ray sources due to dark matter annihilation. We present the self-consistent derivation of the equation of motion of particle in the metrics of primordial black hole immersed into cosmological background. By numerical solution of this equation we find the central dark matter density profile. The density growth is suppressed in the central part of the profile compared with previous calculations.

Within the scope of simple cosmological models we have studied the role of spinor field in the evolution of the Universe when it is non-minimally coupled to the gravitational one. If the spinor field nonlinearity describes an ordinary matter such as radiation, the presence of non-minimality becomes essential and leads to the rapid expansion of the Universe in FRW model, but this is not the case for LRSBI model. If the spinor field nonlinearity describes a dark energy the role non-minimal coupling becomes insignificant in both isotropic and anisotropic models.

The coordinate transformations are proposed to transform Gödel and Kerr metrics to a nonrotating form by the uniform way.

Neutron stars contain superdense matter in their interiors. Characteristic densities in their cores are several times higher than the standard density of nuclear matter. This matter is so dense that it would be natural to assume that frequent particle collisions produce immediate equilibration. However, because of the slowness of some reactions, the equilibration with respect to them can be greatly delayed. Then one should deal with non-equilibrium stars which contain extra energy to be released. Deviations from equilibrium can affect neutrino emission of neutron stars, warm up their interiors and influence their thermal evolution. The effects of equilibration can be important for pulsating, rotating, accreting neutron stars, as well as for merging binary neutron stars.

Equilibrium of a gravitating scalar field inside a black hole compressed to the state of a boson matter, in balance with a longitudinal vector field (dark matter) from outside is considered. Analytical consideration, confirmed numerically, shows that there exist static solutions of Einstein’s equations with arbitrary high total mass of a black hole, where the component of the metric tensor $g^{rr}(r)$ changes its sign twice. The balance of the energy-momentum tensors of the scalar field and the longitudinal vector field at the interface ensures the equilibrium of these phases. Considering a gravitating scalar field as an example, the internal structure of a black hole is revealed. Its phase equilibrium with the longitudinal vector field, describing dark matter on the periphery of a galaxy, determines the dependence of the velocity on the plateau of galaxy rotation curves on the mass of a black hole, located in the center of a galaxy.

We have previously shown that the singularity in a Schwarzschild black hole of stellar or larger mass may be avoided in a semiclassical manner by using as a source of gravity the stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, with a minimum spherical radius a few orders of magnitude larger than the Planck length. In this note we estimate the nonlocal contribution to the total SET due to particle creation from vacuum. We show that this contribution is negligibly small as compared to vacuum polarization and does not affect the previously suggested scenario.

The redshift of the spectral lines of electromagnetic radiation of a binary star that moves in the vicinity of a supermassive black hole is considered. An approach for the reconstruction of the relative motion of the components of the binary using observational data of redshift is proposed.

We outline the basic generic features of regular black holes and self-gravitating solitons replacing naked singularities with Dark Energy (DE) interiors, including thermodynamics of horizons and products of black holes evaporation as dark matter candidates with DE interiors, two kinds of interiors for rotating objects, electrically charged black holes and spinning solitons and non-dissipative source of their electromagnetic fields and geometry.

Based on spectropolarimetry for a number of active galactic nuclei in Seyfert 1 type galaxies observed with the 6-m BTA telescope, we have estimated the spins of the supermassive black holes at the centers of these galaxies. We have determined the spins based on the standard Shakura-Sunyaev accretion disk model. More than 70% of the investigated active galactic nuclei are shown to have Kerr supermassive black holes with a dimensionless spin greater than 0.9.

The role of space-time torsion in astrophysics in the frame of minimum gauge gravitational theory in Riemann-Cartan space-time is discussed. The influence of the vacuum torsion on dynamics of astrophysical objects induced by the interaction of their spin momenta with vacuum torsion is studied. Possible manifestations of such interaction are considered.

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters $\mathrm{\Theta }$ and $\beta$ on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of $\beta =\mathrm{\Theta }$ and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of $\beta =\mathrm{\Theta }$ and with charge will be the same but the charge or field need some scaling. Finally, results in the case of $\beta \ne \mathrm{\Theta }$ with charge are completely different. It means that we have other components in addition to having a time component of the field.

The new result on Horndeski model asymptotic at Galaxy cluster scales is presented. As the obtained constraint for ${\mathrm{\Lambda }}_{eff}$ has the same order as for the real cosmological constant we demonstrate that at extra-galactic scales Horndeski model is consistent with existing astrophysical data.

If two particles collide near a rotating black hole, their energy in the centre of mass frame can become unbounded under certain conditions. In doing so, the Killing energy $E$ of debris at infinity is, in general, remain restricted. If $E$ is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. We also discuss the case of a pure electric super-Penrose process that is valid even in the flat space-time. The key role in consideration is played by the Wald inequalities.

Intensities of the gravitational radiation from a coalescence of miniholes and quadrupole transitions of hydrogen-like atoms are calculated. The total energies of the background gravitational radiation from the coalescence of miniholes and the graviatom quadrupole transitions prove to be comparable with that from the coalescence of two stellar mass black holes.

We focus on the consequences of that the Event Horizon Telescope obtained images of the black hole shadow in the center of the M87 galaxy. We show that to test extended theories of gravity the improving of the resolution by 3 orders is necessary. In addition it is demonstrated that the rotation distorts the shape of the shadow and corrections from the extended gravity may affect on this distortion.

We discuss extended model of planetary system formation. Gravitational collapse of protoplanets leads to the formation of planets and their satellite systems. We consider the hypothesis of a two-stage mechanism of formation of satellite system. Small satellites are formed from the remnants of a collapsing protoplanetary cloud, and large satellites are formed by capturing other relatively small protoplanets. In this paper we study the process of formation of the initial gas-dust cloud, whose evolution leads to the formation of a protoplanetary, and then a planetary system. The justification of the extended model is carried out by numerical simulation. Stable for some time configurations are obtained as a result of interaction of the oncoming mass flows: the spatial collisionless matter takes a lens-like shape, and the planar dissipative system tends to form two gravitating rotating bodies, like the binary stars.