Neutral Test Particles Research Articles

Gravitational energy of a noncommutative Vaidya black hole

In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

ON THE RELATIVISTIC PRECESSION AND OSCILLATION FREQUENCIES OF TEST PARTICLES AROUND RAPIDLY ROTATING COMPACT STARS

Whether analytic exact vacuum(electrovacuum) solutions of the Einstein(Einstein-Maxwell) field equations can accurately describe or not the exterior spacetime of compact stars remains still an interesting open question in Relativistic Astrophysics. As an attempt to establish their level of accuracy, the radii of the Innermost Stable Circular Orbits (ISCOs) of test particles given by analytic exterior spacetime geometries have been compared with the ones given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EoS). It has been so shown that the six-parametric solution of Pach\'on, Rueda, and Sanabria (2006) (hereafter PRS) is more accurate to describe the NS ISCO radii than other analytic models. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, as well as the precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries; then we compare them with the numerical values obtained by Morsink and Stella (1999) for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole (BH) and NS signatures as well as probe the nuclear matter EoS and NS parameters from the Quasi-Periodic Oscillations (QPOs) observed in Low Mass X-Ray Binaries.

Path and path deviation equations for p-branes

Abstract Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises à la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions.

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: Analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr\"om space-time in terms of the Weierstra\ss{} $\ensuremath{\wp}$, $\ensuremath{\sigma}$, and $\ensuremath{\zeta}$ elliptic functions. Based on the study of the polynomials in the $\ensuremath{\vartheta}$ and $r$ equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstr\"om space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstr\"om space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

Circular motion of neutral test particles in Reissner-Nordström spacetime

We investigate the motion of neutral test particles in the gravitational field of a mass $M$ with charge $Q$ described by the Reissner-Nordstr\"om (RN) spacetime. We focus on the study of circular stable and unstable orbits around configurations describing either black holes or naked singularities. We show that at the classical radius, defined as $Q^2/M$, there exist orbits with zero angular momentum due to the presence of repulsive gravity. The analysis of the stability of circular orbits indicates that black holes are characterized by a continuous region of stability. In the case of naked singularities, the region of stability can split into two non-connected regions inside which test particles move along stable circular orbits.

Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in general relativity

We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner-Nordstr\"{o}m field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges $q$ and $Q$, respectively, the conditions of attraction (when $qQ>0$) and repulsion (when $qQ<0$) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, stability conditions for such static equilibrium states are found. It is shown that stable states are possible only for the bound states of weakly charged particles in the field of a naked singularity. Frequencies of small oscillations of test particles near their equilibrium positions are also found.

Innermost stable circular orbits around magnetized rotating massive stars

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.

Singular densities, test particles and generalized Hamiltonian systems in general relativity

We derive the motion equations and the structure equations of neutral and charged test particles, starting from the gravitational field equations. The method consists in the application of conservation laws to singular tensor densities, which represent regions of strong matter concentration. Moreover, a Hamiltonian formulation of the particle equations is given, in the form of implicit differential equations generated by Hamiltonian Morse families.

General-relativistic radial motions of neutral and charged test particles in the field of a charged spherically symmetric object

General-relativistic radial motions of charged and neutral test particles in the Reissner-Nordstrom field are investigated and classified. The conditions for suspension of such particles over the central source and stability of such equilibrium static states are studied. It is shown that stable states are only possible for the bound states of weakly charged particles in the field of an extremely charged central source.

A model for linear dragging

We try to carry over, as closely as possible, the well-known results for rotational dragging (Thirring, Brill and Cohen) to dragging due to linearly accelerated masses. To this end, a spherical, charged mass shell is linearly accelerated by a (weak) external, axisymmetric and dipolar charge distribution. It is shown that the interior of this (Reissner–Nordström-like) shell stays flat. The dragging of neutral test particles inside the shell, defined by their acceleration, scaled by the overall acceleration of the (rigid) shell, is calculated for the weak field case for a highly massive but weakly charged shell and for the general strong field case. The results compare favourably with the corresponding results for rotational dragging.

Traversable Lorentzian wormholes in the vacuum low energy effective string theory in Einstein and Jordan frames

Three new classes (II-IV) of solutions of the vacuum low energy effective string theory in four dimensions are derived. Wormhole solutions are investigated in those solutions including the class I case both in the Einstein and in the Jordan (string) frame. It turns out that, of the eight classes of solutions investigated (four in the Einstein frame and four in the corresponding string frame), massive Lorentzian traversable wormholes exist in five classes. Nontrivial massless limit exists only in class I Einstein frame solution while none at all exists in the string frame. An investigation of test scalar charge motion in the class I solution in the two frames is carried out by using the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Sawicki theorem. A curious consequence is that the motion around the extremal zero (Keplerian) mass configuration leads, as a result of scalar-scalar interaction, to a new hypothetical ``mass'' that confines test scalar charges in bound orbits, but does not interact with neutral test particles.

Exact relativistic static charged dust discs and non-axisymmetric structures

The well-known ‘displace, cut and reflect’ method used to generate discs from given solutions of Einstein field equations is applied to the superposition of two extreme Reissner–Nordström black holes to construct discs made of charged dust and also non-axisymmetric planar distributions of charged dust on the z = 0 plane. They are symmetric with respect to two or one coordinate axes, depending on whether the black holes have equal or unequal masses, respectively. For these non-axisymmetric distributions of matter we also study the effective potential for geodesic motion of neutral test particles.

Notes on applications of general relativity in free space : implication from the motion of a test particle

The equations of motion of a neutral test particle in the field obtained by Wanas (1990) are completely solved. The solution obtained is compared with corresponding solutions in the cases of the Reissner-Nordstrom field, the Kerr field, and the Kerr-Newman field. The comparison shows that the new constant, appeared in the field considered, is connected to electromagnetism and not to spin phenomena.

Shock wave mixing in Einstein and dilaton gravity

We consider possible mixing of electromagnetic and gravitational shock waves, in the Planckian energy scattering of point particles in Minkowski space. By boosting a Reissner-Nordström black hole solution to the velocity of light, it is shown that no mixing of shock waves takes place for arbitrary finite charge carried by the black hole. However, a similar boosting procedure for a charged black hole solution in dilation gravity yields some mixing the wave function of even a neutral test particle, acquires a small additional phase factor depending on the dilatonic black hole charge. Possible implications for poles in the amplitudes for the dilaton gravity case are discussed.

Gravitational energy of a stringy charged black hole

It is known that a static, spherically symmetric stringy charged black hole has several different properties than that of the Reissner-Nordström black hole. In this letter we obtain the gravitational energy of the stringy charged black hole and observe that the total energy is positive and is confined to the interior of the black hole. This is in contrast to the result for the Reissner-Nordström black hole, where the total gravitational energy is positive but is shared by its interior as well as exterior. Consequently, unlike the case of the Reissner-Nordström black hole, the effective gravitational mass experienced by a neutral test particle situated at any finite distance in the gravitational field of the stringy charged black hole is positive.

The gravitational field of string matter

We analyze the static gravitational field of a body (the string star) made of a large number of massive scalar states of the superstring. We consider two cases, one in which these states are neutral string excitations, massive already in ten dimensions, and one in which their masses (and charges) originate in the process of compactification on tori. In both cases the gravitational field is modified by the presence of other massless fields that couple to the string star matter. These fields, and the strength of their couplings, are fixed by superstring perturbation theory and may be infered by studying the scattering of a neutral massless test particle. We compute the deflection angle up to second order in Newton's constant, and by a comparison with field theory explicitly show which among the various massless fields of the superstring are excited by the string star matter. The perturbative series can now be resummed by finding the exact solution to the classical equations of motion of the corresponding low-energy action. We discuss the exact solutions in some detail.

Equations of motion and orbit perturbations of a neutral particle in a quasi-isotropic Kerr metric

In this paper, using a quasi-isotropic from the Kerr metric, we have deduced the equations of motion of a neutral test particle in the gravitational field of a spherical homogeneous rotating body. The perturbation equations of the particle's orbit have also been derived.

Gravitational anyon

We show that, in the (2+1)-dimensional Einstein gravity without the Chern-Simons term, the topological interaction of a point source with or without spin necessarily makes the composite state of the source and neutral test particle a gravitational anyon. In particular for a massless spinning source with spin $\ensuremath{\sigma}$, the angular momentum $l$ of the gravitational anyon is given by $l=n\ensuremath{-}\frac{\ensuremath{\sigma}E}{2\ensuremath{\pi}}$, where $E$ is the energy and $n$ is an integer.

The geodesics of the Kaluza-Klein wormhole soliton

The Kaluza-Klein wormhole soliton metric is a regular localized solution with Minkowskian signature, to the sourceless five-dimensional Einstein equations. We apply five-to-three dimensional reduction to convert the problem of geodesic motion of neutral or charged test particles in this metric to a non-relativistic potential problem, which we discuss in detail, studying bound and scattering states. We show that there is no observable difference between scattering of a spinless test particle by a point charge and by a wormhole soliton.

A magnetized object in Kaluza–Klein theory

In this paper, we present a study of the stable equatorial (θ = π/2) and polar [Formula: see text] trajectories of neutral or charged test particles around a magnetized object in five-dimensional Kaluza–Klein theory. We also show how the nature of these trajectories changes with the variation of the angular momentum of the test particles and with the magnetic-field parameter. We point out that the Gaussian curvature tends to infinity at the Matos surface (defined in the text). A comparison is also made between four-dimensional and five-dimensional studies for equatorial and polar trajectories.