Shadows as a tool to evaluate black hole parameters and a dimension of spacetime

Shadow formation around supermassive black holes were simulated. Due to enormous progress in observational facilities and techniques of data analysis researchers approach to opportunity to measure shapes and sizes of the shadows at least for the closest supermassive black hole at the Galactic Center. Measurements of the shadow sizes around the black holes can help to evaluate parameters of black hole metric. Theories with extra dimensions (Randall–Sundrum II braneworld approach, for instance) admit astrophysical objects (supermassive black holes, in particular) which are rather different from standard ones. Different tests were proposed to discover signatures of extra dimensions in supermassive black holes since the gravitational field may be different from the standard one in the general relativity (GR) approach. In particular, gravitational lensing features are different for alternative gravity theories with extra dimensions and general relativity. Therefore, there is an opportunity to find signatures of extra dimensions in supermassive black holes. We show how measurements of the shadow sizes can put constraints on parameters of black hole in spacetime with extra dimensions.     

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.     

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.     

From white dwarfs to black holes (commemorating the 70th anniversary of the theory of compact objects)

We discuss basic ideas which were fundamental for the black hole concept. The major goal of the historical part is an attempt to explain the long way to the birth of the black hole concept, since the black hole solution was already found in 1916 by K. Schwarzschild, but the black hole concept was only introduced in 1967 by J.A. Wheeler. We discuss the basic notations of the black hole theory and observational manifestations of black holes. We analyse the possibility to interpret the very peculiar distortion of the Fe K_α‐line in such a way.     

Extended Far-Infrared CO Emission in the OMC-1 Core of Orion

We report the discovery of quasi-periodic oscillations (QPOs) at roughly 187 and 150 Hz in the X-ray intensity of X-ray nova XTE J1859+226. The source was observed during a recent outburst with the Rossi X-Ray Timing Explorer. Besides these high-frequency QPOs, we have also detected QPOs (and sometimes their harmonics) at 6-7 Hz and significant broadband variability at low frequencies. These properties, as well as the observed hard X-ray spectrum, make XTE J1859+226 a black hole candidate (BHC). The detection of QPOs at two distinct frequencies greater, similar100 Hz in two observations separated by about 4 hr provide additional insights into the high-frequency QPO phenomenon in BHCs. The importance lies in the proposed interpretations, which invariably involve the effects of strong gravity near a black hole. We compare our results to those of other BHCs and discuss the impact of the observational data on the models in a global context.     

Bounding greybody and deflection angle of improved Schwarzschild black hole

In this paper, we study the weak deflection angle in the spacetime of improved Schwarzschild black hole using the method derived by Gibbons and Werner. To do so, we derive the optical curvature from the optical metric and calculate deflection angle in weak field limits by using the Gauss–Bonnet theorem. Moreover, we study the effect of the plasma medium on the weak gravitational lensing using the Gauss–Bonnet theorem. Furthermore, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Moreover, we obtain the bound on greybody for improved Schwarzschild black hole.     

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.     

Where are the X-ray quasi-periodic oscillations in active galaxies?

In this paper, we address the question of whether existing X-ray observations of Seyfert galaxies are sufficiently sensitive to detect quasi-periodic oscillations (QPOs) similar to those observed in the X-ray variations of Galactic black holes (GBHs). We use data from XMM–Newton and simulated data based on the best Rossi X-ray Timing Explorer ( RXTE ) long-term monitoring light curves to show that if X-ray QPOs are present in Seyfert X-ray light curves – with similar shapes and strengths to those observed in GBHs, but at lower frequencies commensurate with their larger black hole masses – they would be exceedingly difficult to detect. Our results offer a simple explanation for the present lack of QPO detections in Seyferts. We discuss the improvements in telescope size and monitoring patterns needed to make QPO detections feasible. The most efficient type of future observatory for searching for X-ray QPOs in active Galactic nuclei (AGN) is an X-ray All-Sky Monitor (ASM). A sufficiently sensitive ASM would be ideally suited to detect low-frequency QPOs in nearby AGN. The detection of AGN QPOs would strengthen the AGN–GBH connection, and could serve as powerful diagnostics of the black hole mass and the structure of the X-ray emitting region in AGN.     

Quasinormal modes of scalar perturbation around a quantum-corrected Schwarzschild black hole

In this paper, we evaluate quasinormal modes (QNMs) of scalar perturbations around a quantum-corrected Schwarzschild black hole by using the third order Wentzel-Kramers-Brillouin (WKB) approximation method. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.     

Schwarzschild black hole in dark energy background

In this paper we present an exact solution of Einstein’s field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type D in the classification of space-times. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the area of the horizons for the Schwarzschild-dark energy black hole.     

黑洞证认的新进展

黑洞是广义相对论的一个重要理论问题，它的存在与否一直是物理学家和天文学家关心的焦点。特别是由于近几年大量先进的观测设备投入使用和观测方法的改进，使得黑洞证认工作有了巨大的进展，成为当今天文学的一个热点。重点综述了恒星级黑洞和星系核的超大质量黑洞的各种天文观测证据，并介绍了与黑洞相关的天体物理学的一些重要前沿。讨论了正在开展的国际重大项目和探索原初黑洞的初步结果，并且展望了未来寻找黑洞天文观测证据的前景和对观测研究的建议。     

Waves in general relativistic two-fluid plasma around a Schwarzschild black hole

Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation.     

Quantum corrections for ABGB black hole

In this paper, we study quantum corrections to the temperature and entropy of a regular Ayón-Beato-García-Bronnikov black hole solution by using tunneling approach beyond semiclassical approximation. We use the first law of black hole thermodynamics as a differential of entropy with two parameters, mass and charge. It is found that the leading order correction to the entropy is of logarithmic form. In the absence of the charge, i.e., e=0, these corrections approximate the corresponding corrections for the Schwarzschild black hole.     

Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths

Submilliarcsecond astrometry and imaging of the black hole Sgr A* at the Galactic Centre may become possible in the near future at infrared and submillimetre wavelengths. Motivated by the observations of short-term infrared and X-ray variability of Sgr A*, in a previous paper, we computed the expected images and light curves, including polarization, associated with a compact emission region orbiting the central black hole. We extend this work, using a more realistic hotspot model and including the effects of opacity in the underlying accretion flow. We find that at infrared wavelengths, the qualitative features identified by our earlier work are present, namely it is possible to extract the black hole mass and spin from spot images and light curves of the observed flux and polarization. At radio wavelengths, disc opacity produces significant departures from the infrared behaviour, but there are still generic signatures of the black hole properties. Detailed comparison of these results with future data can be used to test general relativity and to improve existing models for the accretion flow in the immediate vicinity of the black hole.     

非微扰的极早期宇宙现象学: 共振的原初扰动与非高斯尾巴

在精确宇宙学的时代, 多信使、高精度、小尺度的宇宙学观测在帮助人们从更加深刻的层面理解宇宙极早期的同时, 也给基于线性近似和微扰展开宇宙学扰动理论带来了新的挑战. 近年来, 对原初引力波和原初黑洞的搜寻使得研究人员们对早期宇宙在小尺度上的非线性非微扰过程产生了浓厚的研究兴趣. 综述了在宇宙学小尺度上关于原初黑洞产生以及引力波研究取得的诸多进展, 重点关注了使用Mathieu方程的共振效应来研究小尺度功率谱放大以及诱导产生可观测的原初引力波的方法. 此外, 还尝试探讨了非高斯尾巴对原初黑洞形成的影响. 发现Mathieu方程所具备的共振效应可以提供一种有效的方法来刻画原初宇宙中小尺度的非微扰动力学过程, 从而能够更好地理解原初黑洞的形成以及相关的引力波产生机制. 同时, 非微扰的非高斯性在原初黑洞形成中可能会产生不可忽视的影响.     

Isofrequency pairing of circular orbits in Schwarzschild spacetime in the presence of magnetic field

We study isofrequency pairing of the circular non-geodesic orbits in the vicinity of the Schwarzschild black hole immersed in external asymptotically uniform magnetic field. The dependence of the isofrequency pairing of non-geodesic orbits from the special quantities, such as radius of the innermost stable circular orbits (ISCO), radius of the circular orbits (r _b ) at the limit e(eccentricity)→0, and from the value of the small quantity ξ=(r _b ?r _ISCO) of the particles moving around the Schwarzschild black hole in the presence of the magnetic field has been found. It is shown that presence of the magnetic field gives rise to the r _ISCO and r _b of the particles to be slightly shifted from black hole and the contribution of the quantity ξ decreases the amount of isofrequency pairing of non-geodesic orbits due to the reduction of the surface of the region between the separatrix and circular-orbit duals (COD). We study the dependence of surface of region where particles can move and isofrequency pairing of non-geodesic orbits occur around the Schwarzschild black hole from the magnetic field. We find a decrease of nearly (7–10) % for the maximal values of the magnetic field B～10⁶–10⁷ Gauss in the surface of region where isofrequency pairing occurs around central object with compare to the one around Schwarzschild black hole without magnetic field. This result implies that it makes easier to identify signals through the astrophysical observations of compact objects in the presence of magnetic field.     

Strong-field tests of gravity using pulsars and black holes

The sensitivity of the SKA enables a number of tests of theories of gravity. A Galactic Census of pulsars will discover most of the active pulsars in the Galaxy beamed toward us. In this census will almost certainly be pulsar–black hole binaries as well as pulsars orbiting the super-massive black hole in the Galactic centre. These systems are unique in their capability to probe the ultra-strong field limit of relativistic gravity. These measurements can be used to test the Cosmic Censorship Conjecture and the No-Hair theorem.The large number of millisecond pulsars discovered with the SKA will also provide a dense array of precision clocks on the sky. These clocks will act as the multiple arms of a huge gravitational wave detector, which can be used to detect and measure the stochastic cosmological gravitational wave background that is expected from a number of sources.     

A systematic study of variability in a sample of ultraluminous X-ray sources

We present results from a study of short-term variability in 19 archival observations by XMM–Newton of 16 ultraluminous X-ray sources (ULXs). Eight observations (six sources) showed intrinsic variability with power spectra in the form of either a power-law or broken power-law-like continuum and in some cases quasi-periodic oscillations (QPOs). The remaining observations were used to place upper limits on the strength of possible variability hidden within. Seven observations (seven sources) yielded upper limits comparable to, or higher than, the values measured from those observations with detectable variations. These represented the seven faintest sources, all with   f_x < 3 × 10⁻¹² erg cm⁻² s⁻¹  . In contrast, there are four observations (three sources) that gave upper limits significantly lower than both the values measured from the ULX observations with detectable variations, and the values expected by comparison with luminous Galactic black hole X-ray binaries (BHBs) and active galactic nuclei (AGN) in the observed frequency bandpass (10⁻³–1 Hz). This is the case irrespective of whether one assumes characteristic frequencies appropriate for a stellar mass  (10 M_⊙)  or an intermediate mass  (1000 M_⊙)  black hole, and means that in some ULXs the variability is significantly suppressed compared to bright BHBs and AGN. We discuss ways to account for this unusual suppression in terms of both observational and intrinsic effects and whether these solutions are supported by our results.     

Galactic models and white dwarf populations

We make use of a previous well-tested Galactic model, but describing the observational behaviour of the various stellar components in terms of suitable assumptions on their evolutionary status. In this way we are able to predict the expected distribution of Galactic white dwarfs (WDs), with results which appear in rather good agreement with recent estimates of the local WD luminosity function. The predicted occurrence of WDs in deep observations of selected Galactic fields is presented, and we discuss the role played by WDs in star counts. The effects on the theoretical predictions of different white dwarf evolutionary models, ages, initial mass functions and relations between progenitor mass and WD mass are also discussed.     

The onset of General Relativity: gravitationally redshifted emission lines

We study and quantify gravitational redshift by means of relativistic ray tracing simulations of emission lines. The emitter model is based on thin, Keplerian rotating rings in the equatorial plane of a rotating black hole. Emission lines are characterised by a generalized fully relativistic Doppler factor or redshift associated with the line core. Two modes of gravitational redshift, shift and distortion, become stronger with the emitting region closer to the Kerr black hole. Shifts of the line cores reveal an effect at levels of 0.0015 to 60% at gravitational radii ranging from 10⁵ to 2. The corresponding Doppler factors range from 0.999985 to 0.4048. Line shape distortion by strong gravity, i.e. very skewed and asymmetric lines occur at radii smaller than roughly ten gravitational radii. Gravitational redshift decreases with distance to the black hole but remains finite due to the asymptotical flatness of black hole space–time. The onset of gravitational redshift can be tested observationally with sufficient spectral resolution. Assuming a resolving power of ∼100000, yielding a resolution of ≈0.1 Å for optical and near‐infrared broad emission lines, the gravitational redshift can be probed out to approximately 75000 gravitational radii. In general, gravitational redshift is an indicator of black hole mass and spin as well as for the inclination angle of the emitter, e.g. an accretion disk. We suggest to do multi‐wavelength observations because all redshifted features should point towards the same central mass. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)