Pure Radiation Fields Research Articles

Pure radiation fields admitting nontrivial null symmetries

The sixteen types of geometrical symmetries corresponding to the continuous groups of collineations and motions generated by a null vector n are considered. The common propagation vector of a pure electromagnetic radiation field and a pure gravitational radiation field is chosen to be n. For such radiation fields all the sixteen symmetries are expressed in terms of the Newman–Penrose (NP) spin coefficients and then it is shown that when n is a gradient field there are only five independent symmetries. The existence of these five nontrivial null symmetries is established by finding exact solutions of Einstein–Maxwell field equations when n satisfies freedom conditions and when l of the NP null tetrad (l, m, m̄, n) is shear-free. Thus a class of space-times of pure radiation fields that admit (i) a Ricci collineation which is not a curvature collineation (CC), (ii) a CC which is not a special curvature collineation (SCC), (iii) a SCC which is not an affine collineation (AC), (iv) an AC which is not a motion, and (v) a motion is determined.

Algebraically special, diverging vacuum and pure radiation fields revisited

Einstein's field equations are reduced to two real differential equations for one complex potential $$\phi (\zeta , \bar \zeta , u)$$ . The known classes of vacuum solutions are invariantly characterized in terms of this potential, and a new representation of the Kerr-Schild class of solutions is given.

A New Warrior in the Kingdom

A New Warrior in the Kingdom

Two simple solutions to Einstein's field equations

Metrics of the formds2=dx2+dy2−dt2+N2dz2 are considered and found to contain rotating dust solutions as well as pure radiation fields.

Neutrino fields in Einstein-Cartan theory

The spin-coefficient formalism presented elsewhere is here applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. The geodesics are both extremals and autoparallels. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric.

Some pure radiation filds in general relativity

AbstractA Demianski-type metric investigated in connection with Einstein's field equations corresponding to pure radiation fields. With aid of complex vectorical formalism, a general solution of these fiel equations is obtained. The solution is algebraically spcial. A particular case of the solution is considered which includes many known solutions; among them are the raiationg versions of some of Kinnersley's solutions.

Kerr-Schild-Vaidya fields with axial symmetry

This paper contains the Kerr-Schild-Vaidya fields with axial symmetry (all metric functions independent of Vaidya's coordinateβ) in closed form. The general problem of Kerr-Schild pure radiation fields without any symmetry can be reduced to a single partial differential equation by means of Kerr's theorem.

On space-times admitting a three-parameter isometry group with two-dimensional null orbits

Space-times admitting a three-parameter group of motions acting on two-dimensional null orbits are considered. A coordinate transformation relating the canonical form of the metrics as given by Petrov (1969) and the apparently more general form given by Defrise (1969) is exhibited. For pure radiation fields the space-time is a PP wave. The general vacuum solution with a cosmological constant is found in closed form.

A method to generate algebraically special pure radiation field solutions from the vacuum

A method is proposed to generate solutions of Einstein's field equations for pure radiation fields from the vacuum. The method applies to all algebraically special diverging vacuum metrics, reducing the field equations to a single partial differential equation for one real function. This equation becomes linear if additional assumptions concerning the vacuum metric are made. Several classes of explicit solutions have been found.

Non-Lorentzian electromagnetic quadripotentials for the field of a classical point particle

It is shown that the well-known separation of the electromagnetic field of a classical point particle into velocity-dependent and pure-radiation fields can be obtained in a simple way for the potentials also, if the Lorentz condition is dropped. Two very simple non-Lorentzian expressions are obtained for the potential corresponding to the pureradiation field; one of them unexpectedly is independent of the acceleration. Similar results are obtained also for the potential corresponding to the velocity-dependent field.

Calibration of LiF teflon rods for internal LiF beta-ray dosimetry

Calibration of LiF Teflon rod dosemeters was performed in pure electron radiation fields. The dosemeters were immersed in solutions of 35S, 99Tc, 204Tl, 32P and 90Y. The mean beta -energy covered the range 0.5 to 0.90 MeV. The investigation resulted in calibration factors depending on the mean beta -energy over the entire range studied; the variation was probably due to self-shielding. The results are in good agreement with theoretical calculations by other workers. As it is of interest for in vivo dose measurements to express the doses delivered to the walls of the gastro-intestinal tract the energy calibration was also performed with the dosemeters pressed against the side of the exposure vessel.

Neutrino radiation fields in general relativity

It is shown that there exist Einstein-neutrino fields which are not defined uniquely by the metric of space-time. These fields form a subclass of the neutrino pure radiation fields and are analogous to Peres' exceptional case for Einstein-Maxwell null fields.

The two-component neutrino field in general relativity

The spinor equations for two-component neutrinos in Riemannian space-time are shown to be equivalent to tensor equations analogous to those for an electromagnetic field with a complex current density vector. The structure of the energy-momentum tensor for neutrinos is more complicated than for the Maxwell field, and in constructing exact solutions of the combined neutrino-gravitational equations it has been found necessary to build up the energy-momentum tensor directly from spinor quantities. Exact solutions for pure radiation fields are obtained in the case of conformally flat and cylindrically symmetric space-times, and also for a non-diagonal radiation metric. It is shown that there are no spherically symmetric radiation solutions for the type of neutrino field considered.

Null Electromagnetic Fields in General Relativity Admitting Timelike or Null Killing Vectors

The paper presents a study of stationary null electromagnetic fields coexisting with a dust distribution. Two exact solutions corresponding to pure radiation fields with the propagation vector as the Killing vector are presented.

Statistical electrodynamics

AbstractThe random pure radiation field postulated in an earlier paper is set up in a relativistically invariant manner. The requirement that this field be isotropic in three dimensions makes much of the formalism identical with the theory of isotropic turbulence, as has been noted by a previous author. It is found, however, that the more stringent requirement of invariance under the Lorentz group, together with the fact that the field components satisfy Maxwell's equations, mean that, to within a multiplicative constant, the entire random process is uniquely specified.In accordance with results obtained previously, the constant is effectively identified as Planck's constant. There then results a striking resemblance between the formalism of the present theory, and that of the quantized pure radiation field, with random variables taking the place of operators, and correlations between these random variables taking the place of commutator brackets.The infinite field energy, which arises also in quantum field theory, where, however, it is usually considered to be purely formal, remains a central difficulty of the random theory. It can be shown to be a natural consequence of assuming Maxwell's equations, and it therefore becomes necessary to consider non-linear modifications of these.The connexion between the present results and the inconsistencies of classical and quantum electrodynamics is discussed. Also some new information is obtained concerning the behaviour of thermodynamic quantities under a Lorentz transformation.

Exact solutions of the field equations: twist-free pure radiation fields

This note is intended to give a rough survey of the results obtained in the study of twist-free pure radiation fields in general relativity theory. Here we are using the following Definition. A space-time ( V 4 of signature +2) is called a pure radiation field if it contains a distortion-free geodetic null congruence (a so-called ray congruence ), and if it satisfies certain field equations which we will specify below (e.g. Einstein’s vacuum-field equations). A (null) congruence is called twist-free if it is hypersurface-orthogonal (or ‘normal’). The results listed below were obtained by introducing special (‘canonical’) co-ordinates adapted to the ray congruence. Detailed proofs were given by Robinson & Trautman (1962) and by Jordan, Kundt & Ehlers (1961) (see also Kundt 1961). For the sake of completeness we include in our survey the subclass of expanding fields, and make use of some formulae first obtained by Robinson & Trautman.

Phenomenological Quantum-Electrodynamics

The quantization of the pure radiation field in a uniformly moving refractive medium is carried through both in the Hamiltonian and in the symmetrical four-dimensional form. The total energy and momentum are diagonalized. For a medium velocity larger than $\frac{c}{n}$ there occur photons with negative energy.