Stationary bound states of Dirac particles in collapsar fields

It is the first time stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product in a wide range of gravitational coupling constant. In order to obtain a discrete energy spectrum, we introduce a boundary condition such that the current density of Dirac particles near the “event horizon” is zero.     

Nordström’s scalar theory of gravity and the equivalence principle

General Relativity obeys the three equivalence principles, the “weak” one (all test bodies fall the same way in a given gravitational field), the “Einstein” one (gravity is locally effaced in a freely falling reference frame) and the “strong” one (the gravitational mass of a system equals its inertial mass to which all forms of energy, including gravitational energy, contribute). The first principle holds because matter is minimally coupled to the metric of a curved spacetime so that test bodies follow geodesics. The second holds because Minkowskian coordinates can be used in the vicinity of any event. The fact that the latter, strong, principle holds is ultimately due to the existence of superpotentials which allow to define the inertial mass of a gravitating system by means of its asymptotic gravitational field, that is, in terms of its gravitational mass. Nordström’s theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a “Nordström-Katz” superpotential.     

On the chiral connection between the ferromagnet,the axisymmetric gravitational problem and the SU(2) vacuum gauge field

A single chiral structure is shown to underly several three-dimensional field equations of physics, e.g., the ferromagnet, the stationary axi-symmetric gravitational problem, and the vacuum SU(2) gauge field in the Coulomb gauge. This connection invites cross-fertilization of exact solutions. As illustrations, exact finite energy solutions are obtained for the ferromagnet via the corresponding Weyl, Kerr, and Tominatsu-Sato solutions of Einstein's gravitational equations. Comments are made on the “local gauge invariance” of the ferromagnet and the gravitational field.     

Theory of Gravitational-Inertial Field of Universe

In this paper the basic proposition is a generalization of the metric tensor by introduction of an inertial field tensor satisfying ?_ig_lm ? g_lm;i ≠ 0. On the basis of variational equations a system of more general covariant equations of gravitational-inertial field is obtained. In Einstein's approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems of generl taheory of relativity by means of the new equations give the same results as Einstein's equations. However application of these equations to the cosmologic problem leads to following results: 1. All Galaxies in the Universe (actually all bodies if gravitational attraction is not considered) “disperse” from each other according to Hubble's law. Thus contrary to Friedmann's theory (according to which the “expansion of Universe” began from the singular state with an infinite velocity) the velocity of “dispersion” of bodies begins from the zero value and in the limit tends to the velocity of light. 2. The “dispertion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free bodies in the inertial field - the law of inertia. All critical systems (with Schwarzschild radius) are specific because they exist in maximal inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In the high-potential inertial and gravitational fields the material mass in a static state or in the process of motion with decelleration is subject to an inertial and gravitational “annihilation”. Under the maximal value of inertial and gravitational potentials (= c²) the material mass is completely “evaporated” transforming into a radiation mass. The latter is concentrated in the “horizon” of the critical system. All critical systems –“black holes”- represent geon systems, i.e., the local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown. The Universe is in a state of dynamical equilibrium. Near the external part of its boundary surface a transformation of matter into electromagnetic-gravitational-neutrineal energy (geon mass) takes place. Inside the Universe, in the galaxies takes place the synthesis of matter from geon mass, penetrating from the external part of the world (from geon crown) by means of a tunneling mechanism. The geon system may be considered as a natural entire cybernetic system.     

Global and local horizon quantum mechanics

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical “Hamiltonian” constraint that relates the gravitational radius to the ADM mass, thus giving rise to a “horizon wave-function”. This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner–Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.     

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.     

The creation of the universe as a quantum phenomenon

Quantum creation of massy particles can occur in the cosmological context without cost of energy. This fact is seized upon to construct a causal open homogeneous isotropic cosmology. The universe is conceived as the response of matter and the gravitational field to a spontaneous pointlike disturbance. Its history unfolds in two stages, creation and free expansion. The first stage gives rise to a “fireball.” The free expansion is extrapolated back to the “fireball.” The latter thus replaces the “big-bang,” thereby avoiding an initial singularity. Though not intrinsic to the theory it does suggest the interpretation of the cosmological part of the gravitational field as the scalar dilaton that is encountered in the dynamical generation of mass in conformally invariant theory.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

Self-gravitating cosmons

In the framework of the SO (1,3)-Yang-Mills gauge theory of gravity, the gravitational gauge field for a non-interacting homogeneous and isotropic matter distribution decouples in the high energy limit (the “asymptotic freedom of gravity”). In this limit, the gauge field equations have non-trivial and completely regular solutions, called “cosmons”; their form and physical interpretation is discussed.     

Hybrid helicity and magneto-vorticity flux conservation in superdense npe-plasma

In this paper, it is shown that the magnetic helicity dissipation per unit volume, coupled with the longitudinal conductivity, causes enhancement of the kinematic rotation of the electric (and magnetic) lines if the npe-plasma vorticity vector aligns with the electric (or the magnetic) field. In the case of a rigidly rotating npe-plasma under the influence of a strong magnetic field, the electric lines are rotating faster than the magnetic lines. It is deduced that the orthogonality of the electric and magnetic fields is an essential condition for the conduction current to remain finite in the limit of infinite electric conductivity of the npe-plasma. In this case, the magnetic field is not frozen into the npe-plasma, but the magnetic flux in the magnetic tube is conserved. The hybrid helicity is conserved if the “magneto-vorticity” vector is tangent to the level surfaces of constant entropy per baryon. The “magneto-vorticity” lines are rotating on the level surfaces of constant entropy per baryon due to the electromagnetic energy flow in the direction of the npe-plasma vorticity and the chemical potential variation locked with the kinematic rotation of the npe-plasma flow lines. In the case of an isentropic npe-plasma flow, there exists a family of timelike 2-surfaces spanned by the “magneto-vorticity” lines and the npe-plasma flow lines. In this case, the electric field is normal to such a family of timelike 2-surfaces. Maxwell like equations satisfied by “magneto-vorticity” bivector field are solved in axially symmetric stationary case. It is shown that the npe-plasma is in differential rotation in such a way that its each plasma shell (i.e., plasma surface spanned by “magneto-vorticity” lines) is rotating differentially without continually winding up “magneto-vorticity” lines frozen into the npe-plasma. It is also found that gravitational isorotation and Ferraro’s law of isorotation are intimately connected to each other because of coexistence of both the plasma vorticity and the magnetic field due to interaction between the electromagnetic field and npe-plasma flows.     

Two-dimensional colloidal mixtures in magnetic and gravitational fields

This mini-review is concerned with two-dimensional colloidal mixtures exposed to various kinds of external fields. By a magnetic field perpendicular to the plane, dipole moments are induced in paramagnetic particles which give rise to repulsive interactions leading to complex crystalline alloys in the composition-asymmetry diagram. A quench in the magnetic field induces complex crystal nucleation scenarios. If exposed to a gravitational field, these mixtures exhibit a brazil–nut effect and show a boundary layering which is explained in terms of a depletion bubble picture. The latter persists for time-dependent gravity (“colloidal shaking”). Finally, we summarize crystallization effects when the second species is frozen in a disordered matrix which provides obstacles for the crystallizing component.     

A new energy source originating from extra dimensions

In this work the Einstein gravitational field equations and the Lichnerowicz boundary formalism in the extra dimensions are used to build up our black hole model from 6-dimensional space－time. From the internal stress－energy tensor the solutions with energy levels and semiclassical space-quantization are obtained, which combines with only one metric condition outside the defect. We show a new type of energy source, which originates from extra dimensions. A part of the energy source of quasi-stellar object (QSO) maybe come from extra dimensions in that way. The theoretical arithmetic upper limit is identical to that of the output energy of QSO.     

The Weiss variation of the gravitational action

The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel geometric derivation of the Weiss variation for the gravitational action: the Einstein–Hilbert action plus the Gibbons–Hawking–York boundary term. In particular, we use the first and second variation of area formulas (we present a derivation accessible to physicists in an “Appendix”) to interpret and vary the Gibbons–Hawking–York boundary term. The Weiss variation for the gravitational action is in principle known to the Relativity community, but the variation of area approach formalizes the derivation, and facilitates the discussion of time evolution in General Relativity. A potentially useful feature of the formalism presented in this article is that it avoids an explicit 3 \(+\) 1 decomposition in the bulk spacetime.     

New field equations in the 5-dimensional projective unified field theory

New field equations of the Projective Unified Field Theory are presented which avoid potential difficulties of former versions with respect to the equivalence principle. The physical interpretation of this new version remains unchanged: constancy of the “gravitational constant”, electromagnetic polarization of the vacuum, definiteness of the energy of the stationary scalaric field, etc. Furthermore, the Klein-Gordon field and the Dirac field are treated.     

Effect of sizes of “bowtie” composite nanoantenna elements on above-threshold photoemission spectra

Strong field effects occurring during the interaction of femtosecond laser pulses with “bowtie” composite nanoantennas are numerically simulated. The effect of the nanoantenna shape and laser pulse parameters on the “plateau” formation in the photoelectron energy spectra is studied. It is shown that the upper boundary of the “plateau” can increase appreciably for the same laser pulse parameters when nanoantenna element sizes are different. Physical explanation of the phenomenon is given.     

Diagonal Metrics of Static, Spherically Symmetric Fields: The Geodesic Equations and the Mass-Energy Relation from the Coordinate Perspective

The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate time and an account of “gravitational acceleration from the coordinate perspective”. The results are applied to the Schwarzschild metric and to the so-called exponential metric. In an attempt to add an account of “gravitational force from the coordinate perspective”, the special relativistic mass-energy relation is generalized to diagonal metrics involving location dependent and possibly anisotropic light speeds. This move requires a distinction between two aspects of the mass of a test particle (parallel and perpendicular to the field). The obtained force expressions do not reveal “gravitational repulsion” for the Schwarzschild metric and for the exponential metric.     

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

Generalized, or “power-law”, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.