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 quark confinement from general relativity

By assuming covariance of physical laws under (discrete) dilatations, it seems possible to describe strong and gravitational interactions in a unified way. An Einstein-type equation with “cosmological” term is for instance suggested for strong field inside hadrons, which yields - among other things - a classical quark confinement in a very natural way. Further consequences are briefly discussed.     

Classical and quantum two-body problem in general relativity

The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different Schwarzschild radii. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.Revised version of Trieste preprint IC/80/124 (August 1980).A similar approach is being developed by a number of authors (see, e.g., References [9] and [10]); the reader will find a comprehensive bibliography in References [11] and [8].     

Classical general relativity derived from quantum gravity

The existence of long range macroscopic attractive forces between masses implies the existence of a mediating helicity ± 2 particle in special relativistic quantum particle theory. It is shown that this fact alone, without assuming the existence of an underlying tensor field, uniquely determines the long wavelength structure of quantum gravitation to be that of Einstein's theory. This equivalence is shown by deriving, from the Ward identities associated with the graviton propagator, the tree graph structure of the graviton-graviton and graviton-matter interaction and establishing that the classical Einstein action is the generating functional. Some properties of closed loop effects are also exhibited.     

Spinor theory of general relativity without elementary gravitons

We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ_μ^α. Our theory has no elementary spin-2 quanta, but does reproduce Einstein's general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.     

Classical models of elementary particles with spin

Classical models of elementary particles, regarded as the ultimate constituents of the known particles, are considered in the framework of general relativity. The work is based on that of López, using the Kerr-Newman solution of the Einstein field equations.     

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.     

Classical and quantum general relativity: A new paradigm

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework. Fifth Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

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 exact solution for uniformly accelerated particles in general relativity

Recently an exact solution of Einstein's empty-space equations referring to four uniformly accelerated particles was given. The relation of this to static axially symmetric metrics of the Weyl and Einstein-Rosen classes is investigated in the present paper. A physical interpretation of the singularity along half of the axis of symmetry of the uniformly accelerated metric in Weyl's form is given. An exact solution corresponding to an expanding (contracting) singular null surface is obtained by a limiting process from that for uniformly accelerated particles.     

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.     

Gravitational interaction of two spinning particles in general relativity. II

Within the framework of the previous paper, we complete the set of equations of motion by including the spin propagation equation at first order. We check this equation with the known result on the precession, which is obtained by means of slow motion approximation of our result. A new scheme of expanding equations of motion is also introduced. It will be useful to undertake higher-order calculations.     

Lagrangian dynamics of spinning particles and polarized media in general relativity

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.     

Non-static spherically symmetric clusters of particles in general relativity: I

In an ingenious way rotation (but no angular momentum) has been introduced in the case of spherical symmetry by Einstein, who has considered a stationary cluster of particles moving freely under the influence of the gravitational field produced by all of them together. The aim of the present work is to extend his idea to the non-static case, and it seems that under some circumstances instead of an indefinite gravitational collapse there is a minimum of the volume and a bouncing back.     

Republication of: The mechanics of matter particles in general relativity

This is an English translation of the first of two papers by Myron Mathisson, first published in German in 1931 and 1937, in which he presented the correct formulation of equations of motion of spinning bodies in general relativity (today known as the Mathisson–Papapetrou equations). The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note and Mathisson’s brief biography, both written by Andrzej Trautman.     

Gravitational radiation reaction on the motion of particles in general relativity

We examine the problem of deducing the geodesic motion of test particles from Einstein's vacuum field equations and its extension to include gravitational radiation reaction. In the latter case we obtain an equation of motion for a particle which incorporates radiation reaction of the electrodynamical type, but due to shearing radiation, together with a mass-loss formula of the Bondi-Sachs type.Work supported in part by the National Science Foundation under Grant PHY-8306104.     

A note on the Lagrangian formalism of spinning particles in general relativity

A Lagrangian formalism of spinning particles in general relativity is given. The (extended) configurational space is chosen to be the Lorentzbundle, and a Lagrangian is constructed from the presymplectic potential of Künzle's canonical dynamics.