An exact solution for uniformly accelerated particles in general relativity

We present an exact solution of the Einstein empty-space equations referring to four particles in relative motion. The particles move with different uniform accelerations relative to a co-ordinate system which is Minkowskian at infinity, except in certain directions. If positive and negative masses are allowed, the particles can move freely under their own gravitation; if all four masses are positive, stresses extending to infinity are needed to cause the motion, but two of the particles can move freely. There are three results of interest. First, the field can be described in terms of a classical potential which is the average of retarded and advanced potentials corresponding to the particles. Secondly, the field at spatial infinity is entirely different from that of a static mass, and theg _ik fall off like the inversesquare of the distance. Thirdly, the world-lines of free particles are geodesics of the space-time.     

Physical properties of an exact spherically symmetric solution with shear in general relativity

The properties of an exact spherically symmetric perfect fluid solution obtained in non-comoving coordinates are examined. This solution contains shear, and the pressure and the density are positive in the interior of the fluid. Their respective gradients with respect to comoving radial coordinate are equal and negative, and the speed of sound in this fluid is less than the speed of light in vacuum and is increasing outwards. There is a singularity at the center of the fluid since the pressure and the density become infinite there, though their ratio becomes unity. This singularity is naked, since there does not exist a trapped surface in the fluid outside this singularity. The circumference is an increasing function of radical comoving coordinate, and the mass function is positive and is increasing outwards. There are no tidal forces in radial direction, but the tidal forces normal to this direction are non-vanishing. We also give the kinematic quantities for this fluid. However, it is not possible to match this solution with an exterior vacuum Schwarzschild solution. Moreover, the dominant energy condition produces imaginary values for the sound speed.     

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 exact solutions for a charged fluid sphere in general relativity

A new generation technique is elaborated in the case of static spherically symmetric distribution of charged fluid. The above technique deals only with a charged perfect fluid verifying a barytropic equation of state, i.e.,P=(γ−1)ρ. Many new exact solutions have then been generated from those of Pant and Sah, Banerjee and Santos, Humi and Mansour. Their physical properties are then studied in some detail.     

Regular exact models for a nonstatic gas sphere in general relativity

Some new exact models for an expanding or a contracting gaseous sphere (i.e., the density is to vanish at the outer boundary together with the pressurep) are given. The physical properties of the models are investigated, and it is found that both the pressure and the density are positive inside the outer boundary of the sphere, and their respective gradients are negative. The density is increasing for contracting spheres, and it is decreasing for expanding spheres. It is also shown that this is the case for the pressure at any moment for the layers close to the boundary of the spheres. For these layers it is further shown that the adiabatic speed of sound is less than the speed of light, and the trace of the energy-momentum tensor is positive. The rate of change of the circumference as measured by an observer riding on the boundary of the sphere is increasing for expanding spheres and it is decreasing for collapsing spheres. We also find that the physical radius is an increasing function of comoving radial coordinate. The mass function is further shown to be positive.     

McGuire-Ruffini solution in new general relativity

We obtain a solution of new general relativity from a solution of Einstein's general relativity which includes many known solutions, such as Kerr-Newman-Kasuya, Kerr-Newman, Kerr, and NUT, as special cases.     

Rotating,charged, and uniformly accelerating mass in general relativity

A new general class of solutions of the Einstein-Maxwell equations is presented. It depends on seven arbitrary parameters that group in a natural way into three complex parameters m + in, a + ib, e + ig, and the cosmological constant λ. They correspond to mass, NUT parameter, angular momentum per unit mass, acceleration, and electric and magnetic charge. The metric is in general stationary and axially symmetric. These solutions are of type D and contain as special cases all known solutions of type D belonging to this class. The known solutions are recovered by performing limiting transitions. An appropriate limit of our solutions describes an electromagnetic field in flat spacetime. We investigate the properties of that field. Its singular region corresponds in general to two circles moving with uniform acceleration in the positive and negative directions along the axis of symmetry. One can easily extend our solutions to the complex domain. Then it turns out that the metric can be written in a double Kerr-Schild form.     

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.     

Elementary particles in bimetric general relativity. II

The possibility of an elementary particle in the framework of classical bimetric general relativity is explored further. A model is considered which is filled with a pressureless primal fluid having a fixed ratio of charge density to mass density. This ratio is assumed to be0, ± ₀ , where ₀ is a universal constant <0.5. If the particle charge is assumed to be ±1/3e, the mass is a fraction of the Planck mass, the fraction being greater than0.0285.     

Minimum size of charged particles in general relativity

Spherical charged matter distributions are examined in a coordinate-free manner within the framework of general relativity. Irrespective of models chosen to describe the interior structure of a charged particle, it is found that the latter's total gravitational mass is positive definite, being finite only when there exists a lower bound for its invariant extension. For a simple choice of matter and charge distributions it is then shown that there is a minimum invariant size for the particle, below which no solution of the field equations exists, the matter density becoming negative and the spacetime developing an intrinsic singularity in the exterior of the particle for radii less than this minimum. A mass renormalization is derived, valid at the moment of time symmetry, which relates the particle's total mass to its charge, bare mass and invariant extension. Our results are compared with those obtained previously by Arnowitt, Deser and Misner, who consider the simpler distribution of a charged spherical shell. Qualitatively, the two situations share the same features. However, in the more realistic spherical distributions the formulae are correspondingly more complicated, and the minimum extension is found to be greater than that of the shell, as one might expect on physical grounds. Moreover, the correspondence between negative valued matter distributions and intrinsic singularities was not evident in the shell case.     

Gravitational interaction of two spinning particles in general relativity

We consider gravitational interaction between two spinning pointlike particles. We use a fastmotion approximation and we obtain the first-order gravitational field and motion equations. Following the method developed by Bel and Martin we get up to the first order: the accelerations, momentum, energy, and a Hamiltonian of the system. This Hamiltonian, when it is expanded in a power series ofc ^–1, agrees with those of earlier authors, who use different techniques.     

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.     

An integrable model in general relativity

Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov exponent calculations for a two-well Duffing oscillator. Received 21 May 2002 / Received in final form 13 September 2002 Published online 29 November 2002     

An axiomatization of general relativity

An axiomatization of the general theory of relativity is proposed. The assumed philosophical background is critical realism. None of the principles commonly considered as founding the theory, such as (a) the equality of inertial and gravitational mass, (b) the principle of equivalence, (c) the principle of general covariance, (d) the geodesic postulate, and (e) Mach's principle, are taken as axioms in our system.     

Exact solution for a static charged gas sphere in general relativity

A general solution of the Einstein-Maxwell field equations has been obtained for a static charged gas sphere having maximum matter density at the centre. The density decreases along the radius and finally becomes zero at the surface of the sphere.     

New exact cylindrical solutions of the Einstein-Maxwell equations of general relativity

We find new exact cylindrical solutions of the Einstein-Maxwell equations, which are cylindrical waves. In some of these solutions Painlevé transcendental functions of type III and V appear. There are maxima in the electromagnetic energy density.     

An exact solution of Einstein's equations for two particles falling freely in an external gravitational field

I begin with a Weyl axially symmetric, static metric representing a spherical particle in equilibrium under the attraction of a semi-infinite rod (s.i.r.) of line density 1/2 and another, pseudo-uniform, gravitational field. A coordinate transformation is then used to remove the s.i.r., enlarge the spacetime, and make the solution time-dependent. The result represents two spherical particles (which do not interact because each is outside the null cone of the other) moving in a certain gravitational wave field. It is shown that the particles move on geodesies of the background wave field. The sources of the wave field are briefly investigated.