Neutrino radiation in spherically-symmetric gravitational fields II. The structure of the radiation field

It is shown that the neutrino radiation field emitted by a star may be described by Vaidya's radiating Schwarzschild metric. The gravitational energy shift of the neutrino field is also considered, both in terms of an exact solution and in the weak field approximation.     

Neutrino radiation in gravitational fields

A differential equation representing radiation solutions of the general relativistic Weyl equation is derived. Their optical properties and the group of motion of the corresponding energy-momentum tensor are studied. If there exists neutrino radiation the Riemann space must be algebraically special and the propagation of the neutrinos occurs only along one of the principal null directions. Gravitational- and neutrinopp-waves taken together, represent an exact solution of the Weyl-Einstein system of field equations.     

Neutrino radiation in spherically-symmetric gravitational fields I. The energy-momentum tensor for the one-neutrino and many-particle neutrino field

The physical situation of a star emitting neutrinos is considered. Some difficulties in the classical theory are mentioned, and a more detailed approach to the properties of neutrino radiation in general relativity is given. The classical theory is here regarded as a one-particle theory, and by summing over many particles propagating in randon radial directions, the energy-momentum tensor of the total radiation field is shown to approximate to the geometrical optics type satisfying other conditions defining its radial and time dependence.     

Neutrino wave packet propagation in gravitational fields

We discuss the propagation of neutrino wave packets in a Lense–Thirring metric using a gravitational phase approach. We show that the neutrino oscillation length is altered by gravitational corrections and that neutrinos are subject to helicity flip induced by stellar rotation. For the case of a rapidly rotating neutron star, we show that absolute neutrino masses can be derived, in principle, from rotational contributions to the mass-induced energy shift, without recourse to mass generation models presently discussed in the literature.     

Neutrino radiation fields in general relativity

All space-times admitting a neutrino radiation field are obtained. Three classes of such space-times exist, characterised by the Weyl tensor being of type D, N (or O) or III.     

Neutrino oscillations in the gravitational field

We calculate the gravitational correction to the phase difference between neutrino mass eigenstates for the spherically symmetric gravitational field described by the Schwarzschild metric. This correction was calculated in a number of works, but the results of these works differ from each other. Our result does not coincide with the results ever published. In this work, we make calculations in the simplest way and verify our result by several tests.     

Neutrino radiation by an electon in quantizing nuclear and strong magnetic fields

The probability and intensity of neutrino radiation of a hydrogen-like atom in the strong magnetic field B >> Z ²α² B ₀, α = e ² = 1/137, B ₀ = m ²/e = 4.41⋅10¹³ G are determined. The temperature dependence of the intensity of an atom ensemble is analyzed.     

Comparison of two definitions of gravitational radiation

In this paper a comparison of two general-covariant definitions of gravitational radiation is made: one of these is based on using the Isaacson tensor, and the other is constructed on the basis of gravitoinertial reference systems.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 68–71, April,1977.In conclusion I take this opportunity to thank V. E. Rodichev and D. D. Ivanenko for valuable critical remarks.     

Field theory III. Energy spectrum and stationary orbit elements in central gravitational fields

The field-dynamical equilibrium equation is solved for the case of a particle moving within the bounded sphere of influence of the gravitational field of a central body. It is shown that under these conditions a system of stationary orbits exists, the fundamental indices of which are the multiplicities of the specific total energy and specific angular momentum squared relative to a certain energy packet and a certain quantum of action, respectively, which are constants of the given system. A tight analogy is noted between the resulting analytical expressions and the well-known (for microsystems) Bohr postulates, quantization rules for elliptical orbits, and spatial quantization rules. In addition, two more quantum numbers are postulated, which completely determine the position of a stationary orbit in a system associated with a central body. As an illustration in support of the theoretical inferences, results are given from an analysis of astronomical data on the distribution of the planets and asteroids with respect to their average distances in the system of a central body, i.e., the sun. This analysis very sharply delineates a hitherto unknown law corresponding to the analytical formulas obtained for gravidynamically equilibrium orbits. It is hypothesized that a much closer analogy exists between the physical substance of the mechanical phenomena in planetary and atomic systems than is customarily acknowledged at the present time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 36–44, August, 1972.The author is indebted to State Prize Laureate Prof. D. D. Ivanenko, Prof. A. F. Bogorodskii, Lecturer V. K. Drofe, Candidate of Physicomathematical Sciences N. A. Yakovkin, and all those who contributed generously to the present study through their critical comments and valuable Suggestions.     

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.     

Neutrino in matter and external fields

A technique for describing various processes proceeding in matter and involving neutrinos and electrons is discussed. This technique is based on “the method of exact solutions,” which implies the use of solutions to proper Dirac equations for particle wave functions in matter. Exact solutions for the neutrino and the electron in the cases of uniform nonmoving and rotating matter are discussed. On studying relativistic neutrino motion and associated neutrino-energy quantization in rotating matter, a semiclassical interpretation of particle finite motion is developed. In the general case of neutrino and electron motion in matter with varying parameters, the corresponding effective force acting on the particles is determined. The possibility of electromagnetic-wave radiation by an electron that moves in a dense neutrino flux of varying density and which is accelerated by this kind of force is predicted.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VI_h cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (–1) is imposed in the particular case of Bianchi VI₀ string models. Various physical and kinematical properties of the models are discussed.     

Neutrino flavor conversion in random magnetic fields

If massive neutrinos possess magnetic moments, a magnetic field can cause a spin flip. In the case of Dirac neutrinos the spin flip converts an active neutrino into a sterile one and vice versa. By constrast, if neutrinos are Majorana particles, a spin flip converts them to a neutrino of a different flavor. We examine the behavior of neutrinos in a random magnetic field as it occurs, for instance, in certain astronomical objects, such as an active galactic nucleus. Both Dirac and Majorana neutrinos behave ergodically: independently of their initial density matrix, they tend towards an equipartition of the helicity states. As a result, about half of the Dirac neutrinos produced becomes sterile. For Majorana neutrinos, there will be an approximate equipartition of flavors, independently of the production mechanism.     

Singularities in Weyl gravitational fields

The peculiarities of the scalarS ≡R _ijkl R ^ijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields. By examiningS along curved families of trajectories to the Weyl singularities, examples are found which contradict previous claims by Gautreau and Anderson regarding ‘directional singularities’. Proper circumferences about the Bach and Weyl line-mass singularity are also examined. There is no apparent correlation between the source structure and the behaviour ofS from this analysis.     

Mass-energy in static gravitational fields

The mass-energy equation in static gravitational fields is shown to beE =g ₄₄ mc ², which agrees with the expressionE =m ₀ c ²(dx/ds)ξ_μ for the energy in a gravitational field possessing a timelike Killing vector ξ. For the Schwarzschild field this leads toE _s ?m ₀ c ² + 1/2m ₀ v ² ?km ₀ M/r. For the Reissner-Nordström field an additional term describing the interaction between the mass and the charge is found to be 2πkm ₀ Q ²/c ² r ². In the Kerr-Newman case more terms are found due to the central rotating gravitating mass.     

Dynamics of a gravitational field. III

The paper investigates the dynamic characteristics of a system of confined sources with gravitational radiation. The gravitational forces acting on test particles, the energy density, the total energy of the system and the total flux of gravitational energy are calculated. These determinations are compared with those carried out previously in the investigations of other authors.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 47–54, August, 1973.