Schwarzschild and Synge once again

We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by J. L. Synge in 1950 to its clarification.Comment: 2 pages, LaTeX, submitted for publication; 2 references, one Note, and an Acknowledgement are adde

Discrete space-time geometry and skeleton conception of particle dynamics

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete geometry is nonaxiomatizable and multivariant. The equivalence relation is intransitive in the discrete geometry. The particles are described by world chains (broken lines with finite length of links), because in the discrete space-time geometry there are no infinitesimal lengths. Motion of particles is stochastic, and statistical description of them leads to the Schr\"{o}dinger equation, if the elementary length of the discrete geometry depends on the quantum constant in a proper way.Comment: 22 pages, 0 figure

Quantum vacuum fluctuations and dark energy

It is shown that the curvature of space-time induced by vacuum fluctuations of quantum fields should be proportional to the square of Newton's constant $G$. This offers a possible explanation for the success of the approximation $G m^6 c^2 h^{-4}$ for the dark energy density, with $m$ being a typical mass of elementary particles.Comment: Changed conten

A General Relativistic Rotating Evolutionary Universe - Part II

As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the generalised Gaussian metric imply in the use of a non-constant temporal metric coefficient modifying Robertson-Walker's standard form. Experimental predictions are madeComment: 7 pages including front cover. Publishe

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to "optical" metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.Comment: 24 pages, accepted for publication in GR

Phenomenological constraints on Lemaitre-Tolman-Bondi cosmological inhomogeneities from solar system dynamics

We, first, analytically work out the long-term, i.e. averaged over one orbital revolution, perturbations on the orbit of a test particle moving in a local Fermi frame induced therein by the cosmological tidal effects of the inhomogeneous Lemaitre-Tolman-Bondi (LTB) model. The LTB solution has recently attracted attention, among other things, as a possible explanation of the observed cosmic acceleration without resorting to dark energy. Then, we phenomenologically constrain both the parameters K_1 = -\ddot R/R and K_2 = -\ddot R^'/R^' of the LTB metric in the Fermi frame by using different kinds of solar system data. The corrections $\Delta\dot\varpi$ to the standard Newtonian/Einsteinian precessions of the perihelia of the inner planets recently estimated with the EPM ephemerides, compared to our predictions for them, yield K_1 = (4+8) 10^-26 s^-2, K_2 = (3+7) 10^-23 s^-2. The residuals of the Cassini-based Earth-Saturn range, compared with the numerically integrated LTB range signature, allow to obtain K_1/2 = 10^-27 s^-2. The LTB-induced distortions of the orbit of a typical object of the Oort cloud with respect to the commonly accepted Newtonian picture, based on the observations of the comet showers from that remote region of the solar system, point towards K_1/2 <= 10^-30-10^-32 s^-2. Such figures have to be compared with those inferred from cosmological data which are of the order of K1 \approx K2 = -4 10^-36 s^-2.Comment: LaTex2e, 18 pages, 3 tables, 3 figures. Minor changes. Reference added. Accepted by Journal of Cosmology and Astroparticle Physics (JCAP

On the complete analytic structure of the massive gravitino propagator in four-dimensional de Sitter space

With the help of the general theory of the Heun equation, this paper completes previous work by the authors and other groups on the explicit representation of the massive gravitino propagator in four-dimensional de Sitter space. As a result of our original contribution, all weight functions which multiply the geometric invariants in the gravitino propagator are expressed through Heun functions, and the resulting plots are displayed and discussed after resorting to a suitable truncation in the series expansion of the Heun function. It turns out that there exist two ranges of values of the independent variable in which the weight functions can be divided into dominating and sub-dominating family.Comment: 21 pages, 9 figures. The presentation has been further improve

Einstein's "Zur Elektrodynamik..." (1905) Revisited, with Some Consequences

Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But with regard to "place" in describing motion, he assumed without analysis the concept of a system of co-ordinates. In the present paper, we propose a way of giving physical (operational) meaning to the concepts of "place" and "co-ordinate system", and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system "in uniform motion of translation relatively to the former". Without assuming "the properties of homogeneity which we attribute to space and time", we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, "one-way" and "two-way" velocities of light, symmetry, the "group property" of inertial reference frames, length contraction and time dilatation, and the "twin paradox". Finally, we point out a flaw in Einstein's argument in the "Electrodynamical Part" of his paper and show that the Lorentz force formula and Einstein's formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck's formula for mass suffices. (Except for the reference to Planck's formula, we restrict ourselves to Physics of 1905.)Comment: 55 pages, 4 figures, accepted for publication in "Foundations of Physics

Neutron stars in generalized f(R) gravity

Quartic gravity theory is considered with the Einstein-Hilbert Lagrangean $R+aR^{2}+bR_{\mu \nu}R^{\mu \nu},$ $R_{\mu \nu}$ being Ricci\'s tensor and R the curvature scalar. The parameters $a$ and $b$ are taken of order 1 km$^{2}.$ Arguments are given which suggest that the effective theory so obtained may be a plausible approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. As in the standard Oppenheimer-Volkoff calculation the star mass increases with increasing central density until about 1 solar mass and then decreases. However a dramatic difference exists in the behaviour of the baryon number, which increases monotonically. The calculation suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.Comment: Keywords: stars, neutron stars; gravity; modified gravity Accepted in Astrophysics and Space Scienc

Conformally coupled dark matter

Dark matter is obtained from a scalar field coupled conformally to gravitation; the scalar being a relict of Dirac's gauge function. This conformally coupled dark matter includes a gas of very light ($m\approx 2.25\times 10^{-34} eV$) neutral bosons having spin 0, as well as a time-dependent global scalar field, both pervading all of the cosmic space. The time-development of this dark matter in the expanding F-R-W universe is investigated, and an acceptable cosmological behaviour is obtained.Comment: LaTEX File 10 pages, no figure