Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10⁸ ÷10⁹ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.     

Regular Magnetic Black Hole Gravitational Lensing

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics,photons do not follow null geodesics of background geometry; but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational lensing is also discussed.     

Weak gravitational lensing of Dilaton-de Sitter black holes

In this work, we examine the effects of the cosmological constant and a scalar field on the angle of deflection of null geodesics in the equatorial plane of the Dilaton-de Sitter space–time. We employ the Rindler–Ishak method to compute the gravitational lensing. We derive new limits on the value of the cosmological constant, \(\Lambda \), based on the bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. These results are essential and important for studies of cosmology.     

Effect of null aether field on weak deflection angle of black holes

We study light rays in the static and spherically symmetric gravitational field of the null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle formed by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations indicate how gravitational lensing is affected by the NAT field. We also illustrate that the bending of light stems from global and topological effects.     

Light’s bending angle due to black holes: from the photon sphere to infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray’s impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.     

Nonlinear-electrodynamic effects in the electromagnetic field of a rotating pulsar

This paper is concerned with the calculation of nonlinear-electrodynamic effects in the field of a rapidly rotating pulsar. For an electromagnetic wave, exact and asymptotic equations of electrodynamic rays and the law thereof are proposed. The time for the nonlinear-electrodynamic delay is shown to be 3.5 times greater than that for rapidly rotating pulsars or pulsars at rest and the angle of nonlinear-electrodynamic bending of rays is shown to be higher by almost 1.7 times.     

Strong field gravitational lensing by a stringy charged black hole

In this paper, we study gravitational lensing of magnetically charged black hole of string theory as a strong field approximation for the supermassive black hole at the center of NGC4486B. We evaluate light deflection angle numerically, from which we obtain magnifications, Einstein rings and observables for the relativistic images. Finally, we explore time delay between relativistic images when they are on the same as well as opposite side of the lens. It is concluded that charge parameter plays a prominent role in the strong gravitational lensing.     

Interstellar Magnetic Fields

Methods of investigating interstellar magnetic fields in spiral galaxies are reviewed. Linearly polarized radio continuum emission yields information about strength and structure of the field. Data are available for our Galaxy and several nearby galaxies. The field strengths vary between 3 and 13 , ?G; a correlation with the average surface mass density of the galaxies is indicated. The field of M31 is probably concentrated in a ring-like torus, as predicted by the dynamo theory. The field structure of M33, however, appears to be bisymmetric as expected in the primordial theory of field origin. Other candidates for a bisymmetric field structure are M51, M81, M83, NGC 2903, and NGC 6946, but the observations are not yet conclusive. The magnetic field in IC 342 is too complicated to be described in terms of a simple model. The interaction processes between the field and the various components of interstellar gas should be investigated in more detail.     

广义相对论浅释(1)

本文用通俗的方法介绍了广义相对论的基本思想 ,并得到了史瓦西场时空弯曲的规律及质点在史瓦西场中自由运动的规律 ,从而解决了引力红移 ,CS原子钟环地球飞行后与地面上 CS原子钟的时差 ,行星进动 ,光子经过太阳表面时的偏转角 ,雷达回波延迟等问题 .     

Magnetostatic wave propagation in a double-layered film structure under inclined magnetic field

Under inclined magnetic field, the propagation characteristics of magnetostatic waves (MSWs) for a double-layered waveguided structure are theoretically studied by using surface permeability method. A new concept called ‘mode interlamination coupling’ is proposed by analysis of mode spectrum, which develops a generalized understanding of the MSWs propagating in a layered structure. A similar treatment can be applied to the situation of multi-layered structure under inclined field. In addition, the dispersion relation and delay characteristics of coupled mode in two different YIG films are studied by numerical analogue at inclination angle from 5 to 20°. The results indicate that the MSWs propagating in double-layer structure is appropriate for high frequency range (8.4∼10 GHz) under inclined field, and it has an optimum range of delay rate superior to single film by adjusting the inclination angle of the magnetic field. Apparently, the performances of double-layered film structure under inclined field have potential dominance in channelization and stability of signal processing for the application of magneto-optic waveguided devices in the future.     

Black hole in an asymmetric electromagnetic field: New ponderomotive effects — Spin precession and drift

Two new ponderomotive effects in black hole physics are indicated: (i) the precession of the rotation axis of a charged black hole in an external magnetic field, (ii) the drift of a non-charged rotating hole in an asymmetric homogeneous electromagnetic field posessing a non-zero Poynting vector. The precession time for a black hole of solar mass with Q = 10^?5M in a magnetic field B ～ 10¹²G is about a year.     

Gravitational Lensing in a Model of Nonlinear Electrodynamics: The Case for Electrically and Magnetically Charged Compact Objects

The astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated. Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coincide with the linear case and it becomes hard to identify the effect of nonlinearity. However, the calculation of the redshift has shown that while the increase in the electric field leads to a decrease in the gravitational redshift,the presence of the strong magnetic field contributes to the gravitational redshift in an increasing manner.     

Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.     

Magnetic fields in spiral galaxies

Radio polarization observations have revealed large-scale magnetic fields in spiral galaxies. The average total field strength most probably increases with the rate of star formation. The uniform field generally follows the orientation of the optical spiral arms, but is often strongest outside the arms. Long magnetic-field filaments are seen, sometimes up to a 30 kpc length. The field seems to be anchored in large gas clouds and is inflated out of the disk, e.g. by a galactic wind. The field in radio halos around galaxies is highly uniform in limited regions, resembling the structure of the solar corona. The detection of Faraday rotation in spiral galaxies excludes the existence of large amounts of antimatter. The distribution of Faraday rotation in the disks shows two different large-scale structures of the interstellar field; axisymmetric-spiral and bisymmetric-spiral, which are interpreted as two modes of the galactic dynamo driven by differential rotation     

Strong Field Gravitational Lensing in a Magnetic Charged Reissner-Nordstr?m Black Hole Pierced by a Cosmic String

The principal focus of this paper is to study the strong field gravitational lensing in a magnetic charged Reissner-Nordstr?m black hole based on the method of cosmic string. We obtain the new coefficients including the tension of the cosmic strings, the strong field deflection limit coefficients, the deflection angle and the magnification, and obtain the relationship between the cosmic string parameter and the new coefficients. The result shows that the cosmic strings have some important effect on the gravitational lensing in a black hole when they pierce it.     

New insights into AGNs with low-mass black holes and high accretion rates: the case of narrow-line Seyfert 1 galaxies

Narrow-line Seyfert 1 (NLS1) galaxies are believed to harbor low-mass black holes accreting at high rates, and they are therefore important targets when studying the nature of black hole growth, galaxy evolution, and accretion physics. We have rigorously studied the physical properties of a sample of NLS1 galaxies. We briefly review previous findings and present new results, including: (1) The locus of NLS1 galaxies on the M _BH-σ plane, which we find to follow the relation of non-active galaxies after removing objects obviously dominated by outflows. (2) The presence of “blue outliers” which hint at extreme outflows as they would be predicted from merger models. (3) More subtle evidence for winds and outflows across the whole NLS1 population. (4) New correlations and trends which link black hole mass, Eddington ratio and physical parameters of the emission-line region. A new element is added to the eigenvector 1 space based on a principal component analysis, which aims at identifying the main drivers of AGN correlation properties.

     

Central black hole masses of galaxies

In this paper, the stellar velocity dispersions in the host galaxies are used to estimate the central black hole masses for a sample of elliptical galaxies. We find that the central black hole masses are in the range of 10^{(5.5-9.5)}M_⊙. Based on the estimated masses in this paper and those by Woo & Urry (2002) and the measured host galaxy absolute magnitude, a relation, log (M_{BH}/M_⊙) = -(0.25±4.3×10^{-3})M_R + (2.98±0.208) is found for central black hole mass and the host galaxy magnitude. Some discussions are presented.     

Maximizing signal-to-noise and contrast-to-noise ratios in FLASH imaging

This paper presents an analysis of signal-to-noise and contrast-to-noise ratios from small tip angle, gradient reversal (FLASH) imaging. Analytic and numerical techniques are used to determine the delay times and tip angles that maximize signal-to-noise per unit time from a single tissue. Similar procedures are used to determine the delay times and tip angles that maximize both T1-induced and T-2*-induced contrast-to-noise per unit time for a pair of tissues as a function of tissue characteristics and pulse sequence sampling times. The advantage of optimized FLASH imaging over optimized spin-echo imaging is quantitated by comparing signal-to-noise and contrast-to-noise ratios per unit time from the two sequences. Images are used to confirm these numerical results, to compare noise levels resulting from gradient reversals versus 180 degrees rephasing pulses and to assess the possible adverse effects of static magnetic field inhomogeneities on FLASH imaging.     

Strong gravitational lensing by a charged Kiselev black hole

We study the gravitational lensing scenario where the lens is a spherically symmetric charged black hole (BH) surrounded by quintessence matter. The null geodesic equations in the curved background of the black hole are derived. The resulting trajectory equation is solved analytically via perturbation and series methods for a special choice of parameters, and the distance of the closest approach to black hole is calculated. We also derive the lens equation giving the bending angle of light in the curved background. In the strong field approximation, the solution of the lens equation is also obtained for all values of the quintessence parameter \(w_q\). For all \(w_q\), we show that there are no stable closed null orbits and that corrections to the deflection angle for the Reissner–Nordström black hole when the observer and the source are at large, but finite, distances from the lens do not depend on the charge up to the inverse of the distances squared. A part of the present work, analyzed, however, with a different approach, is the extension of Younas et al. (Phys Rev D 92:084042, 2015) where the uncharged case has been treated.     

The gravitational bending of light by stars: a continuing story of curiosity,scepticism, surprise,and fascination

Driven entirely by human curiosity, the effect of the gravitational bending of light has evolved on unforeseen paths, in an interplay between shifts in prevailing paradigms and advance of technology, into the most unusual way to study planet populations. The confirmation of the bending angle predicted by Einstein with the Solar Eclipse measurements from 1919 marked the breakthrough of the theory of General Relativity, but it was not before the detection of the double image of the quasar 0957+561 that ‘gravitational lensing’ really entered the observational era. The observation of a characteristic transient brightening of a star caused by the gravitational deflection of its light by an intervening foreground star, constituting a ‘microlensing event’, required even further advance in technology before it could first emerge in 1993. While it required more patience in waiting before ‘Einstein’s blip’ for the first time revealed the presence of a planet orbiting a star other than the Sun, such detections can now be monitored live, and gravitational microlensing is not only sensitive to masses as low as that of the Moon, but can even reveal planets around stars in galaxies other than the Milky Way.