We investigate the observational signatures of an idealized double-ring and double-torus system orbiting a Schwarzschild black hole, allowing the two emitting components to have mutually inclined symmetry axes. Using general-relativistic ray tracing, we construct frequency-shift maps, bolometric flux maps on the observer's screen, and the corresponding spectral line profiles of the emitted radiation. The single equatorial torus is used as a reference configuration in order to isolate the effect of the second emitting component and of the mutual misalignment of the two structures. We show that the presence of two non-coplanar emitting structures produces characteristic multi-peak spectral profiles and asymmetric bolometric-flux distributions. These signatures are imprinted both in the line-profile morphology and in the α-profiles of the bolometric flux, providing simple diagnostic features of non-coplanar multi-component accretion structures.

We investigate the light curve of an isolated bright spot in a Keplerian orbit around a Kerr black hole candidate to probe possible deviations from the standard event-horizon picture. In particular, we explore the presence of a reflective surface, namely a “mirror” near the horizon, and its observable consequences. We present estimates on the time delays of the echoes of electromagnetic radiation from the mirror or some other reflecting area related to black hole mimickers. Our results show that photon reflections from such a surface imprint distinct late-time features in the light curve, producing an electromagnetic analogue of gravitational wave echoes. For lower values of the spin, the reflected signal appears within the same orbital period and leads to a noticeable enhancement of the flux. In contrast, for higher spins, the effect emerges only after several orbits, giving rise to a characteristic echo-wave train. These features provide a potential observational signature of horizon-scale modifications in compact objects.

Oscillatory behavior in the total flux emitted from both single and double torus structures was observed in our general relativistic magnetohydrodynamical simulations performed using the High-Accuracy Astrophysical Relativistic MHD code. These features became evident during a ray tracing conducted with the postprocessing tool IPOLE. Fast Fourier transform analysis of the resulting light curves revealed the presence of dominant frequency components. Two dominant frequencies are observed for interacting counterrotating tori, demonstrating a frequency ratio ∼3 : 2 that is generated during the most intensive interaction of the tori. For corotating tori, the situation is more complex. There are indications that increasing magnetic field intensity enlarges the number of observed oscillations.

We construct optical appearance and profiled spectral lines of Keplerian discs with inner edge at the innermost circular geodesic located on both sides of reflection-symmetric Simpson-Visser wormholes, in dependence on their parameter and inclination angle of distant observers. We demonstrate significant differences in appearance of the discs on the our side and the other side of the Simpson-Visser wormholes. Large part of the other-side disc is always in dark region of the image of the disc orbiting on the our side, enabling thus a simple distinguishing in observations. The profiled spectral lines generated by the disc on the other side (our side) demonstrate strong (weak) dependence on the spacetime parameter, and weak (strong) dependence on the inclination angle; they have also different shape, giving thus other clues to clearly distinguish in observations reflection-symmetric wormholes as alternatives to black holes.

We analyze the effect of a spherically symmetric clump on the anisotropy of the cosmic microwave background radiation temperature in the framework of the standard model of cosmology with a non-zero cosmological constant Λ and we show that it weakens the Rees-Sciama effect.

We present the analysis how Hořava gravity and plasma influence the strong lensing phenomena around Kehagias–Sfetsos (KS) black holes. Using the semi-analytical Bozza method of strong lensing limit, we determine the multiple images, namely their separation S, and magnification R. We apply our calculations to the case of supermassive black hole having mass $$M=6.5\times 10^{9}\text {M}_\odot $$ and being at distance $$d_0=16.8\text {Mpc}$$ from observer corresponding to those observed in M87. We show that the sensitivity of image magnification, image separation, and shadow angular size on KS parameter $$\omega $$ and plasma parameter k are of order from 1 to $$10\%$$ for R and $$~\,16\%$$ for S.

The Hartle-Thorne (H-T) models of slowly rotating neutron or quark stars, characterized by the mass M, dimensionless spin a, and reduced quadrupole moment q, are constructed for the observationally given rotational frequency frot = 580 Hz (290 Hz) of the compact star in the atoll source 4U 1636-53, and a wide range of equations of state (EoS) giving sequences of allowed states governed by the relations a(M), q(M). These sequences are used in the framework of the resonant switch (RS) model combining pairs of geodesic oscillation models to match the data of the twin high-frequency quasi-periodic oscillations observed in the 4U 1636-53 source. The results of the matching procedure using the H-T models are compared to those based on the Kerr approximation of the exterior of the neutron stars. The best H-T matches fix the only variant of the RS model combining particular modifications of the relativistic precession model, exclude the rotation frequency frot = 290 Hz, restrict the considered EoS to six of them, excluding the strange quark stars, and significantly improve precision of the matches given by any single geodesic oscillations model. The Kerr matching allows two variants of the RS model, thus, giving false information, and only three EoS, thus, giving insufficient information. Our results demonstrate that in the matching procedure, the Kerr approximation can be used only for neutron stars governed by the H-T models with q < 2, implying an important restriction on the applicability of the Kerr approximation for description of the oscillatory phenomena around neutron stars. On the other hand, the RS model is sufficiently discriminating for the spacetime metric to be largely determined by fitting to the data. The ranges of the external spacetime parameters of the neutron stars related to the best H-T matches are determined to be M approximate to 2.10-2.13 M-circle dot , a approximate to 0.21-0.25, q approximate to 1.8-2.3. Most compact neutron star is predicted by the Gandolfi EoS, when M approximate to 2.10 M-circle dot , a approximate to 0.21, q approximate to 1.8, with the equatorial radius R approximate to 10.83 km and eccentricity epsilon = 0.03.

The combined effect of a strong gravitational field and electromagnetic field in the vicinity of a generic regular black hole related to non-linear electrodynamics with Maxwellian weak-field limit on the radiation flux of a hot spot orbiting the regular black hole on the Keplerian disc has been studied. The frequency shift due to the strong gravitational field and magnification of the radiation related to gravitational lensing have been calculated. We compare the flux related to the Maxwellian regular black hole to the flux of the hot spots moving with the same orbital period around standard Schwarzschild and Raissner-Nordstrom black holes to illustrate the role of the effective geometry governing photon motion around the regular black hole.

We consider a simple model of a black hole surrounded by a toroidal structure and experiencing deformation due to magnetic field and the tidal force. For this system we construct the shadows of Preston-Poisson black hole, apply it to supermassive black hole $M87^*$ and compare it with the shadows of corresponding Schwarzschild and Kerr black holes. We find that for large deviation parameters $B$ and $E$ the shadow of Preston-Poisson black hole is clearly distinguishable from Kerr black hole provided the angular resolution of measurements is of order $\mu\mathrm{arcsec}$.

The aim of the present research is the analysis of the photon motion in the regular spacetimes arising as solutions of the Einstein gravity coupled with a non-linear electrodynamics (NED). The photons no longer follow the null geodesic of the background spacetime, but the null geodesics of an effective geometry where the electromagnetic non-linearity is directly reflected in addition to the spacetime geometry. Motion of photons is compared to the motion of neutrinos that are not directly affected by the non-linearities of a non-Maxwellian electromagnetic field, and follow null geodesics of the background spacetime. We determine shadows of the regular Bardeen black holes, representing a special solution of the general relativity coupled with NED related to a magnetic charge, both for photons and neutrinos, and compare them to the shadow of the related Reissner–Nordstrom black holes. We demonstrate that the direct NED effects give clear signature of the presence of the regular black holes, on the level going up to $$20\%$$ that is detectable by recent observational techniques. We also demonstrate strong influence of the NED effects on deflection angle of photons moving in the Bardeen spacetimes, and on the time delay of the motion of photons and neutrinos in vicinity of the black hole horizon.

We study the appearance of Keplerian accretion disks in order to demonstrate the influence of the nonlinear electrodynamics (NED) on the gravitational lensing and frequency shifting of the images of the Keplerian disks. We focus our attention on the Bardeen black hole backgrounds with magnetic charges that could be considered to be acceptable solutions for the Einstein gravitational equations combined with those representing an NED. Photons governing the appearance of the Keplerian disks follow null geodesics of the effective geometry related to the Bardeen spacetime. We compare the appearance governed by the effective geometry to those governed by the spacetime geometry itself, and to the appearance of Keplerian disks orbiting a related Reissner–Nordstrom black hole spacetime. We demonstrate a clear and very strong difference between the disk images determined by the effective geometry and the others, both in the shape and (especially) in the frequency mapping where it exhibits a difference of three orders.

We report on a new class of solutions of black hole accretion disks that we have found through three-dimensional, global, radiative magnetohydrodynamic simulations in general relativity. It combines features of the canonical thin, slim, and thick disk models but differs in crucial respects from each of them. We expect these new solutions to provide a more realistic description of black hole disks than the slim disk model. We are presenting a disk solution for a nonspinning black hole at a sub-Eddington mass accretion rate, . By the density scale-height measure the disk appears to be thin, having a high density core near the equatorial plane of height , but most of the inflow occurs through a highly advective, turbulent, optically thick, Keplerian region that sandwiches the core and has a substantial geometrical thickness comparable to the radius, H ∼ r. The accreting fluid is supported above the midplane in large part by the magnetic field, with the gas and radiation to magnetic pressure ratio β ∼ 1, this makes the disk thermally stable, even though the radiation pressure strongly dominates over gas pressure. A significant part of the radiation emerging from the disk is captured by the black hole, so the disk is less luminous than a thin disk would be at the same accretion rate.

Considering the regular Bardeen black hole spacetimes, we test the observational effects of the general relativistic solutions coupled to non-linear electrodynamics (NED) by studying the photon motion in the effective geometry governed by the spacetime geometry and the NED Lagrangian. We focus our attention to the observationally important case of profiled spectral lines generated by rings radiating in a fixed frequency and orbiting the black hole along circular geodesics of the Bardeen spacetime. Such profiled spectral lines are observed in active galactic nuclei and in microquasars, giving sufficient data for the test of regular black holes. We expect that such radiating rings could arise around the Galaxy central supermassive black hole SgrA*, and the related profiled spectral lines could give important additional information to those obtained by direct observations due to the Event Horizon (GRAVITY) Telescope. We demonstrate that the profiled spectral lines of the radiating rings predict strong signatures of the NED effects on the photon motion – namely the frequency shift to the red edge of the spectrum, and narrowing of the profile, by more than one order in comparison with the case of the profiles generated purely by the spacetime geometry, for all values of the magnetic charge and the inclination angle of the observer. The specific flux is substantially suppressed and for extended Keplerian disks even the shape of the profiled line is significantly modified due to the NED effect.

We study optical phenomena in generic regular, magnetically charged, spherically symmetric black hole spacetimes arising from coupling of the Einstein gravity and nonlinear electrodynamics (NED) with the Maxwellian weak-field limit, where photons follow null geodesics of an effective geometry, directly reflecting the electromagnetic nonlinearity. We compare the motion of photons with that of massless neutrinos, which are not affected directly by nonlinearities of the non-Maxwellian electromagnetic field and follow null geodesics of the background spacetime. We determine shadows of such black holes, compare the time delays of photons and neutrinos moving in their field, and construct images of the Keplerian disks. We demonstrate that in the case of the "Maxwellian" NED black holes the optical phenomena give relevant signatures of the NED effects detectable by GRAVITY or the Event Horizon Telescope, but they are not strong enough to be excluded by recent observations as in the case of regular Bardeen black holes.

The 20th anniversary RAGtime workshop took place at the Silesian University in Opava, Czech Republic on October 15-19, 2018. The scientific focus of the workshop was traditionally devoted mainly to problems of relativistic physics of black holes and neutron or quark stars. Large attention was given to confronting theoretical models with up-to-date observations available through both electromagnetic and gravitational wave window to the Universe. Current issues in accretion theory was explored. Participants furthermore attempted to address problems related to cosmology, mathematical aspects of the theory of relativity, and alternative theories of gravity. Last but not least, special attention was putted on national and international collaboration regarding the present and future cosmic X-ray missions. The workshop included a special public lecture 'How to search for Alien Civilizations in the Galaxy?' given by professor Marek Abramowicz on Tuesday, October 16, 2018.

We construct the light escape cones of isotropic spot sources of radiation residing in special classes of reference frames in the Kerr–de Sitter (KdS) black hole spacetimes, namely in the fundamental class of ‘non-geodesic’ locally non-rotating reference frames (LNRFs), and two classes of ‘geodesic’ frames, the radial geodesic frames (RGFs), both falling and escaping, and the frames related to the circular geodesic orbits (CGFs). We compare the cones constructed in a given position for the LNRFs, RGFs, and CGFs. We have shown that the photons locally counter-rotating relative to LNRFs with positive impact parameter and negative covariant energy are confined to the ergosphere region. Finally, we demonstrate that the light escaping cones govern the shadows of black holes located in front of a radiating screen, as seen by the observers in the considered frames. For shadows related to distant static observers the LNRFs are relevant.

The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordstrom (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.

In the weak field approximation, we study the gravitational lensing near the regular Bardeen, Hayward and Ayon-Beato–Garcia (ABG) black holes surrounded by plasma. The exact expressions for the deflection angle of the photons due to the effect of the gravitational field and the plasma have been obtained. The analysis of the image source brightness magnification in the background spacetimes of (i) Bardeen, (ii) Hayward and (iii) ABG regular black holes have shown that the increase of the corresponding charge of regular black hole causes the increase in the magnification of the source image. In addition to the primary ring, one may observe the secondary ring with smaller magnification. The influence of the plasma with (i) constant and (ii) radial power law electron density to the magnification of the source image has been studied.

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure pc to the central energy density pc, higher than a = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N is an element of (2.138, 4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number > 50, while for smaller values of the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N >= 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10(-3) of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.