Black hole shadow image and visibility analysis of Sagittarius A*

The compact dark objects with very large masses residing at the centres of galaxies are believed to be black holes. Due to the gravitational lensing effect, they would cast a shadow larger than their horizon size over the background; the shape and size of this shadow can be calculated. For the supermassive black hole candidate Sgr A*, this shadow spans an angular size of about 50 μas, which is under the resolution attainable with the current astronomical instruments. Such a shadow image of Sgr A* will be observable at about 1 mm wavelength, considering the scatter broadening by the interstellar medium. By simulating the black hole shadow image of Sgr A* with the radiatively inefficient accretion flow model, we demonstrate that analysing the properties of the visibility function can help us determine some parameters of the black hole configuration, which is instructive for the submillimetre Very Long Baseline Interferometry (VLBI) observations of Sgr A* to be made in the near future.     

Strong gravitational lensing in a charged squashed Kaluza-Klein black hole

In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension ρ ₀ and the charge of black hole ρ _q on these parameters and observables.     

Gravitational waves: The future of black hole physics

The new millennium will witness the operation of several long-baseline ground-based interferometric detectors, possibly a space-based detector too, which will make it possible to directly observe black holes by catching gravitational waves emitted by them during their formation or when they are perturbed or when a binary consisting of black holes in-spirals due to radiation reaction. Such observations will help us not only to test some of the fundamental predictions of Einstein's general relativity but will also give us the unique opportunity to map black hole spacetimes, to measure the masses and spins of black holes and their population, etc.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

A Research on the Gravitational Wave Radiation of OJ 287

The research on quasar OJ 287 has lasted over 100 years. OJ 287 exhibits the phenomenon of periodic two-peak outbursts with the eruptive period of 12 years. Observations are rather well interpreted with the black hole binary model. In this model, the secondary black hole moves around the primary black hole and crashes against the accretion disk of the primary black hole, causing outbursts. This model reasonably explains the light curves of OJ 287 and correctly predicts the time of future outbursts. These indirectly justify the precessional effect of general relativity and the existence of gravitational waves. The massive black hole in the center of galaxy is an important kind of gravitational wave source. However, the number of the galaxies with precisely determined kinematical equations of inner components is quite small. The precise kinematic orbits of black holes are provided by the black hole binary model, so the radiation of gravitational waves can be studied on the basis of these kinematic orbits. Based on the existing work, the evolutionary relations of the radiation power and waveform of gravitational waves with time are first derived by using the post-Newtonian approximation method. According to the current progress of the detection equipment of gravitational waves, i.e., IPTA (International Pulsar Timing Array), the direct detection of gravitational waves from OJ 287 may be possible within the future decade.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

Line Shapes Emitted from Spiral Structures around Symmetric Orbits of Supermassive Binary Black Holes

Variability of active galactic nuclei is not well understood. One possible explanation is existence of supermassive binary black holes (SMBBH) in their centres. It is expected that major mergers are common in the Universe. It is expected that each supermassive black hole of every galaxy eventually finish as a SMBBH system in the core of newly formed galaxy. Here we model the emission line profiles of active galactic nuclei (AGN) assuming that the flux and emission line shape variations are induced by supermassive binary black hole systems (SMBBH). We assume that the accreting gas inside the circumbinary (CB) disk is photo ionized by mini accretion disk emission around each SMBBH. We calculate variations of emission line flux, shifts and shapes for different parameters of SMBBH orbits. We consider cases with different masses and inclinations for circular orbits and measure the effect to the shape of emission line profiles and flux variability.     

Gravitational wave bursts from collisions of primordial black holes in clusters

The rate of gravitational wave bursts from the mergers of massive primordial black holes in clusters is calculated. Such clusters of black holes can be formed through phase transitions in the early Universe. The central black holes in clusters can serve as the embryos of supermassive black holes in galactic nuclei. The expected burst detection rate by the LISA gravitational wave detector is estimated.     

The problem of few black holes

The problem of few black holes becomes important in multiple mergers of galaxies. If supermassive black holes in centres of galaxies are common, then interaction of three or four supermassive black holes should also be common. The merger of two galaxies with one black hole each produces a semi-stable black hole binary system. Subsequent mergers of galaxies with their own central black holes produces dynamical few-body evolution in which mergers of black holes occur. According to our numerical simulations this evolution typically ends when only one or two black holes remain and, in the latter case, they are ejected in opposite directions from the center of the galaxy. Even when we pick the initial black hole masses at random from a wide distribution, the two black hole ejections happen rather symmetrically. Sometimes the final masses differ considerably in which case only the lighter black hole is ejected. This is caused by the potential barrier of the galaxy itself which prevents the heavy slowly moving black hole flying out of the galaxy. We discuss OJ287 as a possible example of a multiple black hole system.     

Relativistic dynamical friction in a collisional fluid

The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is calculated for straight-line motion and circular motion, generalizing previous results by several authors. Possible applications to the study of extreme mass-ratio inspirals around strongly accreting supermassive black holes are suggested.     

Gravitationless black holes

A gravitationless black hole model is proposed in accord with a five-dimensional fully covariant Kaluza-Klein (K-K) theory with a scalar field, which unifies the four-dimensional Einsteinian general theory of relativity and Maxwellian electromagnetic theory. It is shown that a dense compact core of a star, when it collapses to a critical density, suddenly turns off or shields its gravitational field. The core, if its mass exceeds an upper limit, directly collapses into a black hole. Otherwise, the extremely large pressure, as the gravity is turned off, immediately stops the collapse and drives the mantle material of supernova moving outward, which leads to an impulsive explosion and forms a neutron star as a remnant. A neutron star can further evolve into a black hole when it accretes enough matter from a companion star such that the total mass exceeds a lower limit. The black hole in the K-K theory is gravitationless at the surface because the scalar field is infinitely strong, which varies the equivalent gravitational constant to zero. In general, a star, at the end of its evolution, is relatively harder to collapse into a gravitationless K-K black hole than a strong gravitational Schwarzschild black hole. This is consistent with the observation of some very massive stars to form neutron stars rather than expected black holes. In addition, the gravitationless K-K black hole should be easier to generate jets than a Schwarzschild black hole.     

Cosmic microwave background radiation of black hole universe

Modifying slightly the big bang theory, the author has recently developed a new cosmological model called black hole universe. This new cosmological model is consistent with the Mach principle, Einsteinian general theory of relativity, and observations of the universe. The origin, structure, evolution, and expansion of the black hole universe have been presented in the recent sequence of American Astronomical Society (AAS) meetings and published recently in a scientific journal: Progress in Physics. This paper explains the observed 2.725 K cosmic microwave background radiation of the black hole universe, which grew from a star-like black hole with several solar masses through a supermassive black hole with billions of solar masses to the present universe with hundred billion-trillions of solar masses. According to the black hole universe model, the observed cosmic microwave background radiation can be explained as the black body radiation of the black hole universe, which can be considered as an ideal black body. When a hot and dense star-like black hole accretes its ambient materials and merges with other black holes, it expands and cools down. A governing equation that expresses the possible thermal history of the black hole universe is derived from the Planck law of black body radiation and radiation energy conservation. The result obtained by solving the governing equation indicates that the radiation temperature of the present universe can be ∼2.725 K if the universe originated from a hot star-like black hole, and is therefore consistent with the observation of the cosmic microwave background radiation. A smaller or younger black hole universe usually cools down faster. The characteristics of the original star-like or supermassive black hole are not critical to the physical properties of the black hole universe at present, because matter and radiation are mainly from the outside space, i.e., the mother universe.     

X-ray reverberation around accreting black holes

Luminous accreting stellar mass and supermassive black holes produce power–law continuum X-ray emission from a compact central corona. Reverberation time lags occur due to light travel time delays between changes in the direct coronal emission and corresponding variations in its reflection from the accretion flow. Reverberation is detectable using light curves made in different X-ray energy bands, since the direct and reflected components have different spectral shapes. Larger, lower frequency, lags are also seen and are identified with propagation of fluctuations through the accretion flow and associated corona. We review the evidence for X-ray reverberation in active galactic nuclei and black hole X-ray binaries, showing how it can be best measured and how it may be modelled. The timescales and energy dependence of the high-frequency reverberation lags show that much of the signal is originating from very close to the black hole in some objects, within a few gravitational radii of the event horizon. We consider how these signals can be studied in the future to carry out X-ray reverberation mapping of the regions closest to black holes.     

The distribution of supermassive black holes in the nuclei of nearby galaxies

The growth of supermassive black holes by merging and accretion in hierarchical models of galaxy formation is studied by means of Monte Carlo simulations. A tight linear relation between masses of black holes and masses of bulges arises if the mass accreted by supermassive black holes scales linearly with the mass-forming stars and if the redshift evolution of mass accretion tracks closely that of star formation. Differences in redshift evolution between black hole accretion and star formation introduce a considerable scatter in this relation. A non-linear relation between black hole accretion and star formation results in a non-linear relation between masses of remnant black holes and masses of bulges. The relation of black hole mass to bulge luminosity observed in nearby galaxies and its scatter are reproduced reasonably well by models in which black hole accretion and star formation are linearly related but do not track each other in redshift. This suggests that a common mechanism determines the efficiency for black hole accretion and the efficiency for star formation, especially for bright bulges.     

Extreme gravitational lensing near rotating black holes

We describe a new approach to calculating photon trajectories and gravitational lensing effects in the strong gravitational field of the Kerr black hole. These techniques are applied to explore both the imaging and spectral properties of photons emitted from an accretion disc, which perform multiple orbits of the central mass before escaping to infinity. Viewed at large inclinations, these higher-order photons contribute ∼20 per cent of the total luminosity of the system for a Schwarzschild hole, while for an extreme Kerr black hole this fraction rises to ∼60 per cent. In more realistic models, these photons will be reabsorbed by the disc at large distances from the hole, but this returning radiation could provide a physical mechanism to resolve the discrepancy between the predicted and observed optical/ultraviolet colours in active galactic nuclei. Conversely, at low inclinations, higher-order images reintercept the disc plane close to the black hole, so need not be absorbed by the disc if this is within the plunging region. These photons form a bright ring carrying approximately 10 per cent of the total disc luminosity for a Schwarzschild black hole. The spatial separation between the inner edge of the disc and the ring is similar to the size of the event horizon. This is resolvable for supermassive black holes with proposed X-ray interferometery missions such as the Microarcsecond X-ray Imaging Mission (MAXIM), and so has the potential to provide an observational test of strong field gravity.     

The broad Fe Kα line and supermassive black holes

Here we present an overview of some of the most significant observational and theoretical studies of the broad Fe Kα spectral line, which is believed to originate from the innermost regions of relativistic accretion disks around central supermassive black holes of galaxies. The most important results of our investigations in this field are also listed. All these investigations indicate that the broad Fe Kα line is a powerful tool for studying the properties of the supermassive black holes (such as their masses and spins), space–time geometry (metric) in their vicinity, their accretion physics, probing the effects of their strong gravitational fields, and for testing the certain predictions of General Relativity.     

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement.
Our results show that for a primary black hole mass of  ∼10⁶–10⁷ M_⊙  , the black hole mass-ratio   q > 10⁻²  , cusp size ∼1 pc, the tidal disruption rate can be as large as  ∼10⁻²–1 M_⊙ yr⁻¹  . This is at least 10²–10⁴ times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10⁵ yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.     

TheS-shaped limit cycle of accretion disk and quasi-periodic variation of BL Lac object on231

If we adopt the analytical approximation of the full intergrations of thin disk, we obtainS-shaped limit cycle around the supermassive black holes in BL Lac objects. On the basis of this, we explain quasi-periodic outburst of the BL Lac object ON+231. Conclusion is drawn that the accretion of black holes is the possible energy source of ON+231 and its variability is caused by the thermal limit cycle with alternating higher and lower accretion rates onto the black hole.     

Geodesics and geodesic deviation in static charged black holes

The radial motion along null geodesics in static charged black hole space–times, in particular, the Reissner–Nordström and stringy charged black holes, are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space–times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space–time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner–Nordström black holes.     

High-frequency X-ray variability as a mass estimator of stellar and supermassive black holes

There is increasing evidence that supermassive black holes in active galactic nuclei (AGN) are scaled-up versions of Galactic black holes. We show that the amplitude of high-frequency X-ray variability in the hard spectral state is inversely proportional to the black hole mass over eight orders of magnitude. We have analysed all available hard-state data from RXTE of seven Galactic black holes. Their power density spectra change dramatically from observation to observation, except for the high-frequency (≳10 Hz) tail, which seems to have a universal shape, roughly represented by a power law of index −2. The amplitude of the tail,   C _M   (extrapolated to 1 Hz), remains approximately constant for a given source, regardless of the luminosity, unlike the break or quasi-periodic oscillation frequencies, which are usually strongly correlated with luminosity. Comparison with a moderate-luminosity sample of AGN shows that the amplitude of the tail is a simple function of black hole mass,   C _M = C / M   , where   C ≈ 1.25 M_⊙ Hz⁻¹  . This makes   C _M   a robust estimator of the black hole mass which is easy to apply to low- to moderate-luminosity supermassive black holes. The high-frequency tail with its universal shape is an invariant feature of a black hole and, possibly, an imprint of the last stable orbit.