Radiation from a Uniformly Accelerated Charge

The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the energy balance paradox finds its solution.     

Local and Global Light Bending in Einstein's and Other Gravitational Theories

To remedy a certain confusion in the literature, we stress the distinction between local and global light bending. Local bending is a purely kinematic effect between mutually accelerating reference frames tracking the same signal, and applies via Einstein's equivalence principle exactly and equally in Newton's, Einstein's, Nordström's and other gravitational theories, independently of all field equations. Global bending, on the other hand, arises as an integral of local bending and depends critically on the conformal spacetime structure and thus on the specific field equations of a given theory.     

Tensor Expressions for Solving Einstein's Equations by the Method of Sequential Approximation

The main aim of this paper is to develop a mathematical tool for General Relativity (GR). For this purpose useful tensor expressions have been worked out, which considerably ease various calculations using the sequential approximation in Einstein's GR. Based upon these expressions, compact and explicit formulae have been worked out for the covariant and contravariant components of the metric tensor and its determinant.     

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in d dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

The Newtonian theory of spatially unbounded, self-gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space R³ from closed models based (without loss of generality) on a flat torus T³. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous background model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.     

Letter: A Potential for the Lanczos Spintensor in Kerr Geometry

We show a generator of the Lanczos spintensorfor a rotating black hole.     

On the Possibility of Testing the Weak Equivalence Principle with Artificial Earth Satellites

In this paper we examine the possibility of testing the equivalence principle, in its weak form, by analyzing the orbital motion of a pair of artificial satellites of different composition moving along orbits of identical shape and size in the gravitational field of the Earth. It turns out that the obtainable level of accuracy is, realistically, of the order of 10^–10 or slightly better. It is limited mainly by the fact that, due to the unavoidable orbital injection errors, it would not be possible to insert the satellites in orbits with exactly the same radius and that such difference could be known only with a finite precision. The present–day level of accuracy, obtained with torsion balance Earth–based measurements and the analysis of the Earth–Moon motion in the gravitational field of the Sun with the Lunar Laser Ranging technique, is of the order of 10^–13. The proposed space–based missions STEP, SCOPE, GG and SEE aim to reach a 10^–15–10^–18 precision level.     

Clocks and the Equivalence Principle

Einsteins equivalence principle has a number of problems, and it is often applied incorrectly. Clocks on the earth do not seem to be affected by the suns gravitational potential. The most commonly accepted reason given is a faulty application of the equivalence principle. While no valid reason is available within either the special or general theories of relativity, ether theories can provide a valid explanation. A clock bias of the correct magnitude and position dependence can convert the Selleri transformation of ether theories into an apparent Lorentz transformation, which gives rise to an apparent equivalence of inertial frames. The results indicate that the special theory is invalid and that only an apparent relativity exists.     

Addendum to the paper “Closed Spaces in Cosmology”

A few corrections and comments are made upon a previously published paper, on the subject of cosmological models with compact spatial sections.     

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.     

Tree-Level Violation of the Equivalence Principle

Massive particles of spin 0 and 1 violate the equivalence principle (EP) at the tree level. On the other hand, if these particles are massless, they agree with the EP, which leads us to conjecture that from a semiclassical viewpoint massless particles, no matter what their spin, obey the EP. General relativity predicts a deflection angle of 2.63 for a nonrelativistic spinless massive boson passing close to the Sun, while for a massive vectorial boson of spin 1 the corresponding deflection is 2.62.     

Identifying Particle Correlations in Quantum Hall Regime

We introduce a method that allows the disclosure of correlations between particle positions in an arbitrary many‐body system. The method is based on a well‐known simulated annealing algorithm and the proposed artificial distribution technique. Additionally, we investigate correlations in quantum Hall liquids (we consider many‐body wave functions that have been recently determined via the cyclotron subgroup model) and present three‐dimensional plots of configuration probability distributions that have been established from numerical simulations. We demonstrate that the preferred simultaneous positions of particles (configurations of positions, which correspond to large values of a system's probability distribution, ) tend to form complicated geometric structures, which are equivalent to classical Wigner crystals only for Laughlin states. Furthermore, we claim that quantum Hall liquids attributed to non‐Laughlin fillings are correlated on subdomains rather than on a whole particle domain (due to a quantizing magnetic field, which modifies the topology of a system's dynamics). Finally, we characterize Hall‐like internal orders in terms of statistical correlations (one‐dimensional unitary representations of cyclotron subgroups). Our conclusions concerning the stability of many‐body states agree with transport measurements and various numerical studies.     

Energy-Momentum and Equivalence Principle in Non-Riemannian Geometries

We introduce an energy-momentum density vector which is independent of the affine structure of the manifold and whose conservation is linked to observers. Integrating this quantity over time-like surfaces we can define Hamiltonian and momentum for the system which coincide with the corresponding ADM definitions for the case of irrotational Riemannian manifolds. As a consequence of our formalism, a Weak Equivalence Principle version for manifolds with torsion appears as the natural extension to non-Riemannian geometries from the Equivalence Principle of General Relativity.