Minkowski Form Research Articles

ON THE BLACK HOLE INTERIOR SPACETIME

A spacetime endowed with an anisotropic fluid is proposed for the interior of a black hole. The geometry has an instantaneous Minkowski form and is a solution of Einstein's equations with a stress tensor on the r.h.s. obeying all the energy conditions. The interior fluid is compressible, with time dependent shear and bulk viscosity coefficients. The energy density ρ and the "radial" pressure p are proportional to 1/t2, with no pressures on θ- and ϕ- directions. The model leads to a time dependent cosmological constant.

Construction of a Penrose diagram for an accreting black hole

A Penrose diagram is constructed for a spatially coherent black hole that accretes at stepwise steady rates as measured by a distant observer from an initial state described by a metric of Minkowski form. Coordinate lines are computationally derived, and radial lightlike trajectories verify the viability of the diagram. Coordinate dependences of significant features, such as the horizon and radial mass scale, are clearly demonstrated on the diagram. The onset of a singularity at the origin is shown to open a new region in space time that contains the interior of the black hole.

Can a Nonsymmetric Metric mimic NCQFT in e+e- → γγ?

In the nonsymmetric gravitational theory (NGT) the space-time metric gμν departs from the flat-space Minkowski form ημν such that it is no longer symmetric, i.e.gμν ≠ gνμ. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation e+e- → γγ, both theories make the same striking prediction that the azimuthal cross section oscillates in ϕ. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

Can a non-symmetric metric mimic NCQFT in $e^ + e^- \to \gamma \gamma$ ?

In the nonsymmetric gravitational theory (NGT) the space-time metric $g_{\mu\nu}$ departs from the flat-space Minkowski form $\eta_{\mu\nu}$ such that it is no longer symmetric, $i.e.$ $g_{\mu\nu} \ne g_{\nu\mu}$. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation $e^+e^- \to \gamma\gamma$, both theories make the same striking prediction that the azimuthal cross section oscillates in $\phi$. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

Radiation pressure and the linear momentum of the electromagnetic field

We derive the force of the electromagnetic radiation on material objects by a direct application of the Lorentz law of classical electrodynamics. The derivation is straightforward in the case of solid metals and solid dielectrics, where the mass density and the optical constants of the media are assumed to remain unchanged under internal and external pressures, and where material flow and deformation can be ignored. For metallic mirrors, we separate the contribution to the radiation pressure of the electrical charge density from that of the current density of the conduction electrons. In the case of dielectric media, we examine the forces experienced by bound charges and currents, and determine the contribution of each to the radiation pressure. These analyses reveal the existence of a lateral radiation pressure inside the dielectric media, one that is exerted at and around the edges of a finite-diameter light beam. The lateral pressure turns out to be compressive for s-polarized light and expansive for p-polarized light. Along the way, we derive an expression for the momentum density of the light field inside dielectric media, one that has equal contributions from the traditional Minkowski and Abraham forms. This new expression for the momentum density, which contains both electromagnetic and mechanical terms, is used to explain the behavior of light pulses and individual photons upon entering and exiting a dielectric slab. In all the cases considered, the net forces and torques experienced by material bodies are consistent with the relevant conservation laws. Our method of calculating the radiation pressure can be used in conjunction with numerical simulations to yield the distribution of fields and forces in diverse systems of practical interest.

Thermal fluctuations of a quantized massive scalar field in a Rindler background

Thermal fluctuations for a massive scalar field in the Rindler wedge are obtained by applying the point-splitting procedure to the zero temperature Feynman propagator in a conical spacetime. Renormalization is implemented by removing the zero temperature contribution. It is shown that for a field of non vanishing mass the thermal fluctuations, when expressed in terms of the local temperature, do not have Minkowski form. As a by product, Minkowski vacuum fluctuations seen by an uniformly accelerated observer are determined and confronted with the literature.

Weyl Representation of the Space-Time of the Vacuum C Metric when m = 0

By using the imaginary Weyl coordinate method, the whole space-time of the vacuum C metric when m = 0 can be represented by the Weyl coordinate system. In addition, a revised transformation relation between Weyl and Minkowski coordinates has been introduced, and the whole space-time obtained by the Minkowski form of the metric can also be represented by Weyl coordinate system.

Acoustic radiation from the monopole resonance of a bubble excited in a dielectrophoretic levitator by oscillating electric fields.

Dielectrophoretic levitation of bubbles in an insulating liquid appears to be a novel way of studying acoustic radiation from transient bubble volume pulsations. Single bubbles were trapped in a spatially varying dc electric field designed to give stable levitation. A few cycles of a weaker oscillating field were superposed on the levitation field. When the modulation frequency was adjusted for the electric field to excite the monopole resonance, a transient acoustic signature was detected by an electrically shielded hydrophone in the surrounding oil bath. One mechanism for monopole excitation is that the energy of the bubble is increased by the electric field giving a positive electric pressure contribution proportional to the square of the field [P. L. Marston and R. E. Apfel, Phys. Lett. 60A, 225–226 (1977)]. The same result follows from a surface average of the Maxwell stress using the Minkowski form of the stress tensor. Additional monopole coupling mechanisms may include a Helmholtz dielectric stress contribution (mitigated by the electrostrictive liquid response) and vertical oscillations of the bubble’s centroid in the hydrostatic pressure field. [Work supported by the Office of Naval Research.]

Möbius transformation and conformal relativity

The Mobius transformation (MT) was analyzed as a coordinate transformation in the Minkowski form. The transformation function contains three separate light cones. The Weyl spheres were interpreted as basic constituents of local light cones. These cones are related to the denominators of the MT and its inverse, and their apexes define an axis with the top of the global light cone as the centerpoint. That axis represents the local part of the world-line of a moving frame of reference. On the world-line, the scale factor of the MT is proportional to the ratio of the radii of the initial Weyl sphere and the equivalent transformed one. The projection centers, defining the transformation of the world-line, were determined graphically. There are two types of such MT's. Inner transformations have their projetion centers on the axes of the frame at rest, outer transformations on the axes of the “observed” moving frame. The signature of x02−r2 is conserved during inner transformations. All possible directions of the world-line of an inertial frame form a timelike “mass cone” around the time axis of the frame at rest. The mass cone and the related spacelike “phase cone” may be seen as projections of a lightlike central motion on the surface of a Weyl sphere. Conformal transformations leave both the mass cone and the phase cone invariant: the MT locally, and the Lorentz transformation globally. The moving frame of any lightlike particle rotates by π/2 radians, thus exchanging the time axis with one of the space axes. The measurable mass of such a particle is considered to be zero because only the central plane of the particle is space-oriented. The real mass is invariant. To test this hypothesis, the two γ-quanta produced by the electron pair annihilation should be led to a recollision, for recreating the initial electron-position pair.

Canonical approach to photon pressure.

A theory of radiation pressure and its effects on the gross motion of an aggregrate of charges is established within a canonical framework. The theory indicates the existence of radiation-pressure effects arising from an additional interaction--the R\ontgen interaction--whose origin is the classical R\ontgen current. A careful development of the formalism reveals the importance of distinguishing between the canonical and mechanical momenta of the gross motion of the aggregate and of incorporating the R\ontgen-type interaction terms when calculating the gross-motion dynamics. A form of the R\ontgen interaction is present even in the dipole approximation: an effect which has previously been ignored but which is necessary to ensure gauge invariance of the radiation-induced mechanical force. Explicit calculations of the rates of change of canonical and mechanical momenta are presented for a general atomic dipole, with specializations to a two-level atom, revealing the presence of velocity-dependent terms in a natural way. The formalism is consistent with the Minkowski form of the classical momentum density of an electromagnetic field.

The meaning of gyroscopic invariance for the electromagnetic energy‐momentum tensor

AbstractThe gyroscopic invariance implies the representation of the antisymmetric part of the Hermite‐symmetric metric by a vector potential. Therefore we introduce the six functions of this antisymmetric part in general as derived by two vector potentials. Then Einstein's variational principle leads to a slight modification of the Einstein‐Schrödinger equations, which just encludes Minkowski's form of the energy‐momentum tensor for the electromagnetic field and the gluon field.

On Lerche's relativistic theory of Poynting's theorem for moving media

view Abstract Citations (1) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On Lerche's relativistic theory of Poynting's theorem for moving media. Ko, H. C. ; Chuang, C. W. Abstract Lerche's (1975) generalization of Poynting's theorem for moving media is critically examined. It is argued that the term proposed by Lerche to represent the work done by a moving transparent medium on the electromagnetic field (and vice versa) appears to be created rather arbitrarily in the analysis and is not based on any physically convincing grounds. It is shown that when this term is combined with Lerche's 'energy density' term, a very simple Minkowski form of Poynting's theorem for moving transparent media is obtained in which the postulated phenomenon does not occur. It is concluded that the physical contents of Lerche's theory are inconsistent with those of both the Minkowski and the Abraham energy-momentum tensors. Publication: The Astrophysical Journal Pub Date: April 1979 DOI: 10.1086/156960 Bibcode: 1979ApJ...229..361K Keywords: Astrophysics; Cosmic Plasma; Magnetohydrodynamics; Plasma Physics; Poynting Theorem; Relativistic Theory; Earth Magnetosphere; Minkowski Space; Pulsars; Astrophysics; Magnetohydrodynamics:Plasma full text sources ADS |

Construction of a left Hilbert algebra with respect to a Minkowski form

We construct a left Hilbert algebra with respect to a Minkowski form and generalize the theorem that every von Neumann algebra is isomorphic to the left von Neumann algebra of a left Hilbert algebra.

Energy - Momentum Tensors for Dispersive Electromagnetic Waves

Classical relativistic field theory is used as a basis for a general discussion of the problem of splitting up the total energy–momentum tensor of a system into contributions from its component subsystems. Both the Minkowski and Abraham forms (including electrostriction) arise naturally in alternative split-up procedures applied to a non dispersive dielectric fluid. The case of an electromagnetic wave in a (spatially and temporally) dispersive medium in arbitrary but slowly varying motion is then treated. In the dispersive case the results cannot be found by replacing the dielectric constant ε with ε(κ, ω) but include derivatives with respect to the wave vector κ and the frequency ω. Ponderomotive force expressions are obtained and the perturbation in the total energy–momentum tensor due to a one-dimensional wavepacket is found. A nonlinear Schrödinger equation is obtained for the evolution of a three-dimensional wavepacket. Both hot and cold plasmas are treated.

Maxwell equations in nonuniformly moving media

The covariant Maxwell equations for material media in arbitrary motion are derived by means of a statistical average of the microscopic equations. Special-relativistic considerations are used throughout, even though accelerated motion is treated. The Minkowski form, originally derived for uniform motion only, is found to be generally valid for nonuniform motion, if the macroscopic quantities are suitably defined. In particular, the covariant polarization is defined in terms of the molecular electromagnetic dipole moments.

Space-Time Structure of a Static Spherically Symmetric Scalar Field

Bergmann and Leipnik have derived some special solutions of the general-relativistic field equations in which the metric has the Schwarzschild or the Minkowski form, although a scalar field is assumed to be present. It will be shown that in reality this scalar field vanishes.