The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.     

The charged line-mass in general relativity

The two exterior solutions for a charged line-mass are examined. In both cases the mass per unit length is negative.     

Static charged dust in general relativity

Solutions of the Einstein-Maxwell equations for static charged dust are discussed. Contrary to what has been asserted earlier it is found that cylindrically symmetric and plane symmetric solutions with the following properties, exist: (a) They are regular in the interior region; (b) the mass density is positive and vanishes at the boundary; (c) the metric, its first derivate, and the electrical field strength are continuous at the boundary; (d) the solutions are mirror symmetric in the plane symmetric case.     

Equilibrium of charged dust in general relativity

Equilibrium of charged dust is studied in both the classical and relativistic theories. It is already known that the configuration of the dust is arbitrary if the ratio of the charge to mass densities,/, is everywhere ± 1 (in relativistic units). I show here that there are equilibrium configurations for certain other values/, including nonuniform ones. The solutions in these cases are arbitrary up to the choice of a harmonic function and a function of the electrostatic potential. In general they contain singularities.     

Nonstatic charged fluid spheres in general relativity

Faulkes has shown that shear-free solutions of the Einstein-Maxwell field equations can be found by solving a single second-order nonlinear differential equation containing two arbitrary functions of the radial coordinate. In this work a very general method is proposed to solve this nonlinear equation which, in effect, extends an earlier work of Wyman to its electromagnetic analog.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

Static charged gas spheres in general relativity

In the present paper the field equations of general relativity have been solved to obtain the different solutions for the static charged gas sphere. These solutions are free from singularities and satisfy the necessary physical conditions.     

Geometry of rotating charged bubbles in general relativity

It is shown that the spatial geometry of the bubbles with a constant radial coordinater _o, embedded in the Kerr-Newman manifold, does not depend on the mass and charge of this solution when referred to a coordinate frame rigidly rotating with the angular velocity =a(r ₀ ^{2+a 2})^–1. The corresponding line element is found to be identical to the one obtained by Smarr for the surface geometry of a charged rotating black hole.     

Elementary particles in bimetric general relativity

A classical model of an elementary particle is considered in the framework of the bimetric general relativity theory. The particle is regarded as a spherically symmetric object filling its Schwarzschild sphere and made of matter having mass density, pressure, and charge density. The mass is taken to be the Planck mass, and possible values of the charge are taken as zero, ±1/3e, ±2/3e, and ±e, with e the electron charge.     

Classical elementary particles in general relativity

Elementary particles, regarded as the constituents of quarks and leptons, are described classically in the framework of the general relativity theory. There are neutral particles and particles having charges±1/3e. They are taken to be spherically symmetric and to have mass density, pressure, and (if charged) charge density. They are characterized by an equation of state P=– suggested by earlier work on cosmology. The neutral particle has a very simple structure. In the case of the charged particle there is one outstanding model described by a simple analytic solution of the field equations.     

New solutions for charged spheres in general relativity

Exact solutions of the Einstein-Maxwell field equations are obtained for the case of static and spherically symmetric distribution of charged matter. The solutions are obtained through the extension of a method originally used for neutral configurations and are conveniently matched to the Reissner-Nordstrom exterior metric. The physical plausability of the solutions is discussed and it is shown that some of them reduce in appropriate limits to known neutral or charged solutions.     

The equilibrium of two charged masses in general relativity

The condition of equilibrium is obtained up to the ppN approximation by solving the Einstein-Maxwell equations. It is conjectured that for spherically symmetric particles the classical condition e₁e₂ = Gm₁m₂ applies.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

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–Nordström 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.     

A solution for a charged sphere in general relativity

In the present paper the field equations of general relativity have been solved to obtain a solution for a static charged fluid sphere. This solution is free from singularity and satisfies the necessary physical conditions.     

Orthonormal tetrads and the charged fluid in general relativity

A space-time filled with the self-gravitating charged fluid with constant electric permitivity and constant magnetic permeability is investigated. On expressing the stress-energy tensor in terms of an orthonormal tetrad, the equations of motion and Maxwell equations are formulated. In case of the geodesic flow, the conditions for divergence-free electric and magnetic fields are obtained. It is shown that the space-time permeated by the charged fluid with the electric field orthogonal to the magnetic one is embedded in 5-dimensional flat class-one space-time if and only if the electromagnetic energy flux vector vanishes.     

General regular charged space-times in teleparallel equivalent of general relativity

Using a non-linear version of electrodynamics coupled to the teleparallel equivalent of general relativity (TEGR), we obtain new regular exact solutions. The non-linear theory reduces to the Maxwell one in the weak limit with the tetrad fields corresponding to a charged space-time. We then apply the energy-momentum tensor of the gravitational field, established in the Hamiltonian structure of the TEGR, to the solutions obtained.