239 research outputs found
Gravitational singularities via acceleration: the case of the Schwarzschild solution and Bach's gamma metric
The so called gamma metric corresponds to a two-parameter family of axially
symmetric, static solutions of Einstein's equations found by Bach. It contains
the Schwarzschild solution for a particular value of one of the parameters,
that rules a deviation from spherical symmetry.
It is shown that there is invariantly definable singular behaviour beyond the
one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal,
timelike Killing vector exists. In this case, a particle can be defined to be
at rest when its world-line is a corresponding Killing orbit. The norm of the
acceleration on such an orbit proves to be singular not only for metrics that
deviate from Schwarzschild's metric, but also on approaching the horizon of
Schwarzschild metric itself, in contrast to the discontinuous behaviour of the
curvature scalar.Comment: 8 pages; text accepted for publication by Astronomische Nachrichte
Electrostatics and confinement in Einstein's unified field theory
A way for appending sources at the right-hand sides of the field equations of
Einstein's unified field theory is recalled. Two exact solutions endowed with
point sources in equilibrium are shown, and their physical meaning is
discussed.Comment: 4 pages, talk given at MG11, Berlin, July 200
The Electrostatics of Einstein's Unified Field Theory
When sources are added at their right-hand sides, and g_{(ik)} is a priori
assumed to be the metric, the equations of Einstein's Hermitian theory of
relativity were shown to allow for an exact solution that describes the general
electrostatic field of n point charges. Moreover, the injunction of spherical
symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges
was proved to yield the equilibrium conditions of the n charges in keeping with
ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of
the theory, since it enters neither the eikonal equation nor the equation of
motion of uncharged test particles. A physically correct metric that rules both
the behaviour of wave fronts and of uncharged matter is the one indicated by
H\'ely. In the present paper it is shown how the electrostatic solution
predicts the structure of the n charged particles and their mutual positions of
electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and
Gravitatio
Time-Varying Fine-Structure Constant Requires Cosmological Constant
Webb et al. presented preliminary evidence for a time-varying fine-structure
constant. We show Teller's formula for this variation to be ruled out within
the Einstein-de Sitter universe, however, it is compatible with cosmologies
which require a large cosmological constant.Comment: 3 pages, no figures, revtex, to be published in Mod. Phys. Lett.
Multidimensional perfect fluid cosmology with stable compactified internal dimensions
Multidimensional cosmological models in the presence of a bare cosmological
constant and a perfect fluid are investigated under dimensional reduction to
4-dimensional effective models. Stable compactification of the internal spaces
is achieved for a special class of perfect fluids. The external space behaves
in accordance with the standard Friedmann model. Necessary restrictions on the
parameters of the models are found to ensure dynamical behavior of the external
(our) universe in agreement with observations.Comment: 11 pages, Latex2e, uses IOP packages, submitted to Class.Quant.Gra
Quantum Tests of the Foundations of General Relativity
The role of the equivalence principle in the context of non-relativistic
quantum mechanics and matter wave interferometry, especially atom beam
interferometry, will be discussed. A generalised form of the weak equivalence
principle which is capable of covering quantum phenomena too, will be proposed.
It is shown that this generalised equivalence principle is valid for matter
wave interferometry and for the dynamics of expectation values. In addition,
the use of this equivalence principle makes it possible to determine the
structure of the interaction of quantum systems with gravitational and inertial
fields. It is also shown that the path of the mean value of the position
operator in the case of gravitational interaction does fulfill this generalised
equivalence principle.Comment: Classical and Quantum Gravity 15, 13 (1998
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