Effective Potential in Noncommutative BTZ Black Hole

In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.     

Hawking Radiation of the Charged Particle via Tunneling from the Kaluza-Klein Black Hole

In this paper, by applying the Lagrangian analysis on the action, we first redefine the geodesic equation of the charged massive particle. Then, basing on the new definition of the geodesic equation, we revisit the Hawking radiation of the charged massive particle via tunneling from the event horizon of the Kaluza-Klein black hole. In our treatment, the geodesic equation of the charged massive particle is defined uniformly with that of the massless particle, which overcomes the shortcomings of its previous definition, and is more suitable for the tunneling mechanism. The highlight of our work is a new and important development for the Parikh-Wilczek’s tunneling method.     

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.     

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.     

On Hawking Radiation via Tunneling from the Reissner-Nordström-de Sitter Black Hole with a Global Monopole

In this paper, we start from the Lagrangian analysis on the action to naturally produce the geodesic equation of the massive particle via tunneling. Then, basing on the new definition for the geodesic equation, we revisit the Hawking radiation of the charged massive particle via tunneling from the Reissner-Nordström-de Sitter black hole with a global monopole. In our treatment, the geodesic equation of the charged massive particle is defined uniformly with that of the massless particle, which overcomes the shortcomings of its previous definition, and is more suitable for the tunneling mechanism. It is noteworthy that, the highlight of our work is a new and important development of the Parikh-Wilczek’s tunneling method.     

Massless spinning test particles in a gravitational field

The classical equations of motion of a massless spinning test particle are derived as a limiting case of Mathisson-Papapetrou equations. It is shown that when a particular supplementary condition is assumed the particle follows a null geodesic and the spin is either parallel or antiparallel to the direction of motion. Moreover, the helicity is conserved in an orientable spacetime. The equations of the propagation of the momentum vector and the spin tensor along the trajectory are given and further implications of the solution are discussed.     

Tidal Effects in Some Regular Black Holes

This paper is aimed to study the tidal forces produced by a class of regular black holes. We consider the radial infall of test particle and find radial as well as angular components of tidal forces by taking geodesic deviation equations. We also compute geodesic deviation vector by solving geodesic deviation equation numerically. It is concluded that a particle undergos either compression or stretching in radial or angular direction due to tidal forces.     

Global attractors for degenerate partial differential equations from nonlinear viscoelasticity

We study several problems for the forced motion of light, uniform, nonlinearly viscoelastic bodies carrying heavy attachments. A ‘reduced’ problem for such motions is obtained by setting the ratio of the inertia of the viscoelastic body to the inertia of the attachment equal to zero. Using methods from infinite-dimensional dynamical systems theory, we prove that the degenerate partial differential equation of this reduced problem has an attractor and that this attractor is contained in an invariant two-dimensional manifold on which solutions are governed by the classical ordinary differential equation for the forced motion of a particle on a massless spring.     

Affine symmetry,geodesics, and homogeneous spacetimes

We show that the conservation laws for the geodesic equation which are associated to affine symmetries can be obtained from symmetries of the Lagrangian for affinely parametrized geodesics according to Noether’s theorem, in contrast to claims found in the literature. In particular, using Aminova’s classification of affine motions of Lorentzian manifolds, we show in detail how affine motions define generalized symmetries of the geodesic Lagrangian. We compute all infinitesimal proper affine symmetries and the corresponding geodesic conservation laws for all homogeneous solutions to the Einstein field equations in four spacetime dimensions with each of the following energy–momentum contents: vacuum, cosmological constant, perfect fluid, pure radiation, and homogeneous electromagnetic fields.     

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.     

Delta-Gravity

We present a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived: Massive particles do not follow a geodesic but massless particles trajectories are null geodesics of an effective metric. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant. Additionally, we study the quantization of the model. The main result being that the Effective Action is finite and receives one loop corrections only.     

Non-relativistic Geodesic Behaviors for a Massive Charged Particle Falling in de Sitter Spacetime

In this article, continuing the work done in the previous paper (Fathi et al. in Int. J. Theor. Phys. 51:1938–1945, 2012), we apply a Lagrangian formalism to demonstrate the shape of the geodesic motions for a massive charged particle which is falling freely in a de Sitter spacetime. We will show that a spiral shape of the trajectory is available, due to the logarithmic behavior of time, with respect to the proper time.     

Spinning test particle in Kalb-Ramond background

In this work we explore the geodesic deviations of spinning test particles in a string inspired Einstein-Kalb-Ramond background. Such a background is known to be equivalent to a spacetime geometry with torsion. We have shown here that the antisymmetric Kalb-Ramond field has a significant effect on the geodesic deviation of a spinning test particle. A search for observational evidence of such an effect in astrophysical experiments may lead to a better understanding of the geometry of the background spacetime.Received: 5 April 2005, Revised: 19 May 2005, Published online: 8 July 2005     

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.     

Schwarzschild黑洞整体正规时空中的测地运动

本文研究了Schwarzschild黑洞整体正规时空中的测地运动,求得了无奇性内部时空中检验粒子测地方程的解析解,并与奇性黑洞情况作了比较。 关键词：     

Lorentz Covariant Canonical Formalism for Free Massive, Massless and Tachyonic Particles

We construct a consistent Lorentz-covariant canonical formalism for a free massive, massless and tachyonic particle in the framework of the absolute synchronization scheme of clocks. In the case of a massive particle our approach is canonically equivalent to the standard formulation which is not manifestly covariant. The absolute synchronization scheme seems to be the only one we can apply in the case of massless and tachyonic particles.     

General properties of the decay amplitudes for massless particles

We derive the kinematical constraints which characterize the decay of any massless particle in flat space-time. We show that in perturbation theory the decay probabilities of photons and Yang-Mills bosons vanish to all orders and the decay probability of gravitons vanishes to one-loop order for graviton loops and to all orders for matter loops. A general power counting argument indicates in which conditions a decay of a massless particle could be possible: the Lagrangian should contain a self-coupling without derivatives and with a coupling constant of positive mass dimension.     

The infeld/schild approach to the geodesic motion of test particles in general relativity

Test particles are defined and a version of the Infeld/Schild theorem on geodesic motion is presented. The hypotheses of the theorem are discussed in the IPN approximation and in the Weyl static axisymmetric metrics. Initial terms in a series solution of the linearized field equations are found explicitly for a test particle on an arbitrary timelike geodesic.     

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.