Motion and collision of particles near Plebanski-Demianski black hole: Shadow and gravitational lensing

Here we consider accelerating and rotating charged Plebanski-Demianski (PD) class of black hole metric as a particle accelerator. We obtain the geodesic motions (timelike, null and spacelike) of particles in a non-equatorial plane around the PD black hole. We find the effective potential, energy, angular momentum, impact parameters, and discuss the circular orbit. We study the center of mass energy of two neutral particles falling from infinity to near the non-extremal horizons (event and Cauchy horizons), extremal horizon, accelerating horizons, and near the center of the PD black hole. Also, we study the collision of a particle and a massless photon. Then we find the center of mass energy due to the collision of two massless photons in the PD black hole background. We compute the redshift and blueshift of the emitted photons by massive particles while light signal travels along null geodesics towards the observer located far away from the source. We study the Penrose process, which occurs within the ergosphere, and examines the particle’s motion with its implications. Here, we analyze the PD black hole shadow’s apparent shape, which forms far away from the black hole. We study the possible visibility of the PD black hole through photon’s shadow and energy emission rate. We also investigate the effect on the shadow of the PD black hole in plasma for a distant observer. We study the strong gravitational lensing by PD black hole. Finally, we analyze the deflection angle, lens equation, position, magnification, Einstein ring and observables by taking the supermassive PD black hole in the Galaxy’s center.     

Kerr-Newman黑洞隧穿辐射的新研究

在文章[吴迪等2013中国科学物理学力学天文学43115]中,从有质量粒子的Lagrangian作用量出发,对Kerr转动黑洞中类时的和类光的测地线方程给出了全新的统一推导,结果表明对转动黑洞隧穿辐射的研究不需要局限地采用拖曳系.这项工作完全克服了先前研究中存在的不足,使得Parikh-Wilczek半经典隧穿方法更加完善和自洽.本文将这一工作推广到转动带电黑洞情形,对Kerr-Newman黑洞中有质量带电粒子测地线方程做了新的推导,并对其隧穿辐射重新做了研究.     

Gödel black hole,closed timelike horizon and the study of particle emissions

We show that a particle, with positive orbital angular momentum, following an outgoing null/timelike geodesic, shall never reach the closed timelike horizon present in the (4 + 1)-dimensional rotating Gödel black hole space–time. Therefore a large part of this space–time remains inaccessible to a large class of geodesic observers, depending on the conserved quantities associated with them. We discuss how this fact and the existence of the closed timelike curves present in the asymptotic region make the quantum field theoretic study of the Hawking radiation, where the asymptotic observer states are a pre-requisite, unclear. However, the semi classical approach provides an alternative to verify the Smarr formula derived recently for the rotating Gödel black hole. We present a systematic analysis of particle emissions, specifically for scalars, charged Dirac spinors and vectors, from this black hole via the semiclassical complex path method.     

Schwarzschild black hole surrounded by quintessence: null geodesics

We have studied the null geodesics of the Schwarzschild black hole surrounded by quintessence matter. Quintessence matter is a candidate for dark energy. Here, we have done a detailed analysis of the geodesics and exact solutions are presented in terms of Jacobi-elliptic integrals for all possible energy and angular momentum of the photons. The circular orbits of the photons are studied in detail. As an application of the null geodesics, the angle of deflection of the photons are computed.     

Investigation the geodesic motion of three dimensional rotating black holes

We study the geodesic equations in the space-time of neutral Brans–Dicke Dilaton black hole in three dimensions and BTZ black hole. We use the process of separation of the Hamilton–Jacobi equation to obtain the constants of motion. The whole analytical solution of the geodesic equations in the space-times of the intended black holes are shown completely. Moreover, the geodesic equations are solved in terms of Weierstrass elliptic functions. Furthermore, with use of the analytical solution and effective potential technique some trajectories around the black holes are classified. Meanwhile, by analytical solution, effective potential and considering the zeroes of underlying polynomials, some possible orbits are plotted. Finally, we compare our results with Cruz et. al. [17] and we indicate the benefits of the analytical method which is applied in this paper.     

On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case. Received: 4 November 1998 / Accepted: 13 February 1999     

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.     

Tidal Forces in Dyonic Reissner-Nrdstrom Black Hole

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordstr¨om black hole.We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles.We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole.The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole.The radial geodesic component starts decreasing in dyonic Reissner-Nordstr¨om black hole unlike Schwarzschild case.We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.     

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.     

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

Propagation of vacuum polarized photons in topological black hole spacetimes

The one-loop effective action for QED in curved spacetime contains equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions lead to a dependence of the photon velocity on the motion and polarization directions. In this paper we investigate the gravitational analogue to the electromagnetic birefringence phenomenon in the static and radiating topological black hole backgrounds. For the static topological black hole spacetimes, the velocity shift of photons is the same as that in Reissner-Nordström black holes. This reflects the fact that the propagation of vacuum polarized photons is not sensitive to the asymptotic behavior and topological structure of spacetimes. For the massless topological black hole and BTZ black hole, the light cone condition remains unchanged. In the radiating topological black hole backgrounds, the light cone condition is changed even for the radially directed photons. The velocity shifts depend on the topological structures. Due to the null fluid, the velocity shift of photons no longer vanishes at the apparent horizons as well as the event horizons. However, the “polarization sum rule” is still valid.     

Pragmatic approach to gravitational radiation reaction in binary black holes

We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into l multipoles to show that all l-metric coefficients are C0 at the location of the particle. Summing over l, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's zeta-function regularization scheme and numerically compute the first-order geodesics.     

Black holes as generalised Toda molecules

In this note we compare the geodesic formalism for spherically symmetric black hole solutions with the black hole effective potential approach. The geodesic formalism is beneficial for symmetric supergravity theories since the symmetries of the larger target space lead to a complete set of commuting constants of motion that establish the integrability of the geodesic equations of motion, as shown in arXiv:1007.3209. We point out that the integrability lifts straightforwardly to the integrability of the equations of motion with a black hole potential. This construction turns out to be a generalisation of the connection between Toda molecule equations and geodesic motion on symmetric spaces known in the mathematics literature. We describe in some detail how this generalisation of the Toda molecule equations arises.     

Vaidya-Bonner黑洞的熵

从零曲面方程出发,得到了VaidyaBonner黑洞的视界;利用KleinGordon方程和薄膜BrickWall模型,并采用WKB近似方法,求出了VaidyaBonner黑洞的熵,所得的熵正好与该黑洞的视界面积成正比. 关键词： 黑洞 熵 薄膜Brick-Wall模型 视界     

黑洞的视界面公式

从零曲面方程出发,导出了黑洞视界面的普遍公式.利用高登方程验证了该公式的正确性,并利用该公式求出了任意加速含荷黑洞的视界. 关键词： 黑洞 视界 零曲面 乌龟坐标变换     

Geodesic motions in extraordinary string geometry

The geodesic properties of the stationary vacuum string solution in (4+1) dimensions with momentum flow along the string direction are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling particle can not arrive at the horizon or singularity. To get into the horizon, a particle need to follow a non-geodesic trajectory. There exist stable null circular orbits and bouncing timelike and null geodesics. In the asymptotic geometry, some geodesics will be repelled by the string contrary to the case of Kerr-Neumann black hole. The light bending effect will be minimized at an impact parameter determined by the angular momentum and energy.     

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek’s semiclassical tunneling method.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) global monopole revisited

In this paper the f(R) global monopole is reexamined. We provide an exact solution for the modified field equations in the presence of a global monopole for regions outside its core, generalizing previous results. Additionally, we discuss some particular cases obtained from this solution. We consider a setup consisting of a possible Schwarzschild black hole that absorbs the topological defect, giving rise to a static black hole endowed with a monopole’s charge. Besides, we demonstrate how the asymptotic behavior of the Higgs field far from the monopole’s core is shaped by a class of spacetime metrics which includes the ones analyzed here. In order to assess the gravitational properties of this system, we analyze the geodesic motion of both massive and massless test particles moving in the vicinity of such configuration. For the material particles we set the requirements they have to obey in order to experience stable orbits. On the other hand, for the photons we investigate how their trajectories are affected by the gravitational field of this black hole.     

Time-like geodesic structure of a spherically symmetric black hole in the brane-world

Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable (unstable) circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressure β and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant α has an impact on its time-like geodesic structure.     

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter, \begin{document}$ \alpha$\end{document} , for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter, \begin{document}$ \alpha$\end{document}; both modify the features of the photon sphere, angle of deflection, and functions \begin{document}$ (\bar{a}$\end{document} and \begin{document}$ \bar{b})$\end{document} owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.