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I deduce an exact and analytic Bianchi type I solution of Einsteins field equations, which generalizes the isotropic LambdaCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the LambdaCDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the LambdaCDM universe model. Although such generalizations of the isotropic LambdaCDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic LambdaCDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic largescale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension., Comment: 28 pages

A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier relativistic paradoxes involving extended bodies or events at different positions. A collision between a rod and a ring impacting at an oblique angle to each other is considered in the context of the special theory relativity. A question arises as to where along the length of the rod the point of impact will be according to two observers following the rod and the ring, respectively. The observers argue from a purely kinematical point of view in favor of two different points of impact along the rod. However there can only exist one point of impact. In order to solve this apparent paradox we use the asynchronous formulation of relativistic kinematics in which the consequences of the relativity of simultaneity are built into the formalism. We show that this reconciles the descriptions from the two frames of reference, and hence that the new paradox leads to a strong argument for the relevance of the asynchronous formulation of relativistic kinematics., Comment: 16 pages and 8 figures

ESA operates the Sentinel-1 satellites, which provides Synthetic Aperture Radar (SAR) data of Earth. Recorded Sentinel-1 data have shown a potential for remotely observing and monitoring local conditions on broad acre fields. Remote sensing using Sentinel-1 have the potential to provide daily updates on the current conditions in the individual fields and at the same time give an overview of the agricultural areas in the region. Research depends on the ability of independent validation of the presented results. In the case of the Sentinel-1 satellites, every researcher has access to the same base dataset, and therefore independent validation is possible. Well documented research performed with Sentinel-1 allow other research the ability to redo the experiments and either validate or falsify presented findings. Based on current state-of-art research we have chosen to provide a service for researchers in the agricultural domain. The service allows researchers the ability to monitor local conditions by using the Sentinel-1 information combined with a priori knowledge from broad acre fields. Correlating processed Sentinel-1 to the actual conditions is still a task the individual researchers must perform to benefit from the service. In this paper, we presented our methodology in translating sentinel-1 data to a level that is more accessible to researchers in the agricultural field. The goal here was to make the data more easily available, so the primary focus can be on correlating and comparing to measurements collected in the broadacre fields. We illustrate the value of the service with three examples of the possible application areas. The presented application examples are all based on Denmark, where we have processed all sentinel-1 scan from since 2016., Comment: 9 pages, 5 figures, conference (AGENG2018)

We study observational viability of Natural Inflation with a tachyon field as inflaton. By obtaining the main perturbation parameters in this model, we perform a numerical analysis on the parameter space of the model and in confrontation with $68\%$ and $95\%$ CL regions of Planck2015 data. By adopting a warped background geometry, we find some new constraints on the width of the potential in terms of its height and the warp factor. We show that the Tachyon Natural Inflation in the large width limit recovers the tachyon model with a $\phi^{2}$ potential which is consistent with Planck2015 observational data. Then we focus on the reheating era after inflation by treating the number of e-folds, temperature and the effective equation of state parameter in this era. Since it is likely that the value of the effective equation of state parameter during the reheating era to be in the range $0\leq \omega_{eff}\leq \frac{1}{3}$, we obtain some new constraints on the tensor to scalar ratio as well as the e-folds number and reheating temperature in this Tachyon Natural Inflation model., Comment: 19 pages, 6 figures, Accepted for publication in JCAP

From a hydrodynamicist's point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (excluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy-Verlinde formula is affected by viscosity., Comment: 71 pages, Invited Review for Int.J.Mod.Phys. D

In order to provide a better understanding of rotating universe models, and in particular the G\"{o}del universe, we discuss the relationship between cosmic rotation and perfect inertial dragging. In this connection, the concept of \emph{causal mass} is defined in a cosmological context, and discussed in relation to the cosmic inertial dragging effect. Then, we calculate the mass inside the particle horizon of the flat $\Lambda$CDM-model integrated along the past light cone. The calculation shows that the Schwarzschild radius of this mass is around three times the radius of the particle horizon. This indicates that there is close to perfect inertial dragging in our universe. Hence, the calculation provides an explanation for the observation that the swinging plane of a Foucault pendulum follows the stars., Comment: 17 pages, 3 figures

John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases. 1. A static, spherically symmetric space, and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe models. We find the general, exact solution of the Nash field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE) in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satifying way of including energy-momentum into the theory has yet to be found., Comment: 7 pages

The research on relativistic universe models with viscous fluids is reviewed. Viscosity may have been of significance during the early inflationary era, and may also be of importance for the late time evolution of the Universe. Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy. We consider also the influence from turbulence, in connection with future singularities of the universe (Big Rip and Little Rip). Finally, we review some recent developments of causal cosmology theories., Comment: 31 pages latex2e, in "Recent Advances in Cosmology", Chapter 4, Nova Science Publishers, 2013

A new source of the C-metric is described using Israel's formalism. This source is a singular accelerated shell. By construction, perfect inertial dragging is realized inside the shell. The equation of state and energy conditions for the shell are discussed., Comment: 20 pages, 6 figures

The concept of negative temperatures has occasionally been used in connection with quantum systems. A recent example of this sort is reported in the paper of S. Braun et al. [Science 339,52 (2013)], where an attractively interacting ensemble of ultracold atoms is investigated experimentally and found to correspond to a negative-temperature system since the entropy decreases with increasing energy at the high end of the energy spectrum. As the authors suggest, it would be of interest to investigate whether a suitable generalization of standard cosmological theory could be helpful, in order to elucidate the observed accelerated expansion of the universe usually explained in terms of a positive tensile stress (negative pressure). In the present note we take up this basic idea and investigate a generalization of the standard viscous cosmological theory, not by admitting negative temperatures but instead by letting the bulk viscosity take negative values. Evidently, such an approach breaks standard thermodynamics, but may actually be regarded to lead to the same kind of bizarre consequences as the standard approach of admitting the equation-of-state parameter w to be less than -1. In universe models dominated by negative viscosity we find that the fluid's entropy decreases with time, as one would expect. Moreover, we find that the fluid transition from the quintessence region into the phantom region (thus passing the phantom divide w=-1) can actually be reversed. Also in generalizations of the LCDM-universe models with a fluid having negative bulk viscosity we find that the viscosity decreases the expansion of the universe., Comment: 7 pages latex, no figures, published electronically in Astrophys. Space Sci

We explore flat {\Lambda}CDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter {\rho}, for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for this model and display them in the s-r-plane.

In this paper we study the evolution of spatially homogeneous and anisotropic Bianchi type-I Universe models with the cosmological constant, \Lambda, and filled with nonlinear viscous fluid. The dynamical equations for these models are obtained and solved for some special cases. We calculate the statefinder parameters for the models and display them in the s-r-plane.

The Levi-Civita Bertotti Robinson (LBR) spacetime is investigated in various coordinate systems. By means of a general formalism for constructing coordinates in conformally flat spacetimes, coordinate transformations between the different coordinate systems are deduced. We discuss the motion of the reference frames in which the different coordinate systems are comoving. Furthermore we characterize the motion of the different reference frames by their normalized timelike Killing vector fields, i.e. by the four velocity fields of the reference particles. We also deduce the formulae in the different coordinate systems for the embedding of the LBR spacetime in a flat 6-dimensional manifold. In particular we discuss a scenario with a spherical domain wall having LBR spacetime outside the wall and flat spacetime inside. We also discuss the internal flat spacetime using the same coordinate systems as in the external LBR spacetime with continuous metric at the wall. Among the different cases one represents a Milne-LBR universe model with a part of the Milne universe inside the wall and an infinitely extended LBR universe outside it. In an appendix we define combinations of trigonometric and hyperbolic functions that we call k-functions and present a new k-function calculus., Comment: 58 pages, 9 figures

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes., Comment: 22 pages, 5 figures

We derive and discuss the physical interpretation of a conformally flat, static solution of the Einstein-Maxwell equations. It is argued that it describes a conformally flat, static spacetime outside a charged spherically symmetric domain wall. The acceleration of gravity is directed away from the wall in spite of the positive gravitational mass of the electric field outside the wall, as given by the Tolman-Whittaker expression. The reason for the repulsive gravitation is the strain of the wall which is calculated using the Israel formalism for singular surfaces., Comment: 11 pages, 0 figures

We deduce general expressions for the line element of universe models with negative and vanishing spatial curvature described by conformally flat spacetime coordinates. The empty Milne universe model and models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual creation of space, matter and energy when conformal time is used in Friedmann-Robertson-Walker models with negative spatial curvature., Comment: 25 pages, 12 figures

We deduce general expressions for the line element of universe models with positive spatial curvature described by conformally flat spacetime coordinates. Models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual annihilation of space, matter and energy in a dust and radiation dominated universe, and continual creation in a LIVE domined universe when conformal time is used in Friedmann-Robertson-Walker models with positive spatial curvature. A general procedure is given for finding coordinates to be used in Penrose diagrams. We also calculate the age and the redshift of some universe models using conformal time., Comment: 22 pages, 9 figures

The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known and also some new transformations to conformally flat spacetime coordinates. A general formula for the recession velocity is deduced., Comment: 12 pages

In the present article we find a new class of solutions of Einstein's field equations. It describes stationary, cylindrically symmetric spacetimes with closed timelike geodesics everywhere outside the symmetry axis. These spacetimes contain a magnetic field parallel to the axis, a perfect fluid with constant density and pressure, and Lorentz invariant vacuum with energy density represented by a negative cosmological constant., Comment: 7 pages, 1 figure

It is demonstrated that energy is conserved during runaway motion of a radiating charge, and during free fall of a charge in a field of gravity. The decisive role of the Schott energy in this connection is made clear. Also it is pointed out that a proton and a neutron fall with the same acceleration in a uniform gravitational field although the proton radiates and the neutron does not., Comment: Version acceptetd for publication in American Journal of Physics. 24 pages. 5 figures

In the standard formulation of the twin paradox an accelerated twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation. Perfect dragging in an exact solution of Einsteins field equations describing flat spacetime inside a shell with Kerr spacetime outside it. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime., Comment: 13 pages

The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known transformations to conformally flat spacetime coordinates, and work out the physical interpretation of conformal coordinate systems in different universe models. We show that continual creation appears when conformal time is used in Friedmann-Robertson-Walker models with negative spatial curvature, and in universe models where the inflationary era started as a quantum fluctuation at t > 0, for example at the Planck time. A general procedure is given for finding coordinates to be used in Penrose diagrams., Comment: Withdrawn by the authors because it has been replaced by new preprints

Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a non-vanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell., Comment: 15 pages, 2 figures, revised and extended

An observer at rest in a uniformly accelerated reference frame experiences a parallel gravitational field, where the rays of light are formed as circular arcs instead of being straight lines. We deduce how a sphere at rest in the Rindler frame, and a freely falling sphere, will appear to an observer at rest in the frame., Comment: 14 pages and 6 figures

In the present article we analyze, by means of the statefinder parameter formalism, some universe models introduced by Brevik and co-workers. We determine constants that earlier were left unspecified, in terms of observable quantities. It is verified that a Big Bang universe model with a fluid having a certain non-linear equation of state behaves in the same way as a model with a viscous fluid., Comment: 15 pages and 1 figure

A charge moving freely in orbit around the Earth radiates according to Larmor's formula. If the path is closed, it would constitute a perpetuum mobile. The solution to this energy paradox is found in an article by C. M. DeWitt and B. DeWitt from 1964. The main point is that the equation of motion of a radiating charge is modified in curved spacetime. In the present article we explain the physics behind this modification, and use the generalized equation to solve the perpetuum mobile paradox., Comment: 9 pages, 3 figures

We consider the perihelion precession and bending of light in a class of Kaluza-Klein models and show that the "electric redshift" model, proposed in Zhang (2006) to explain the redshift of Quasars, does not agree with observations. As Zhang's model only considers the Jordan frame, we also compute the perihelion precession as seen in the Einstein frame and show that, to lowest order, the perihelion precession can only be consistent with observation in the Einstein frame. However, when we consider the corresponding "electric redshift" in the Einstein frame, we find that the redshift is significantly lower than for the Jordan frame and is therefore very unlikely to explain the redshift of quasars., Comment: 12 pages, 3 figures

Analytical properties of a flat universe with cold matter and vacuum energy is presented., Comment: 10 pages, 11 figures

Machs principle and the principle of relativity have been discussed by H. I. Hartman and C. Nissim-Sabat in this journal. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenon of inertial dragging been invoked, and no calculation have been offered by either side to substantiate their claims. Here I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculations to demonstrate how these points come out as consequences of the general theory of relativity, Comment: 17 pages

We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime., Comment: 13 pages, 1 figure

The universe today, with structure such as stars, galaxies and black holes, seems to have evolved from a very homogeneous initial state. From this it appears as if the entropy of the universe is decreasing, in violation of the second law of thermodynamics. It has been suggested by Roger Penrose \cite{grossmann:penrose:wcc} that this inconsistency can be solved if one assigns an entropy to the spacetime geometry. He also pointed out that the Weyl tensor has the properties one would expect to find in a description of a gravitational entropy. In this article we make an attempt to use this so-called Weyl curvature conjecture to describe the Hawking-Bekenstein entropy of black holes and the entropy of horizons due to a cosmological constant., Comment: 10 pages, 2 figures, typesetting revtex4

The interpretation of the expanding universe as an expansion of space has recently been challenged. From the geodesic equation in Friedmann universe models and the empty Milne model, we argue that a Newtonian or special relativistic analysis is not applicable on large scales, and the general relativistic interpretation in terms of expanding space has the advantage of being globally consistent. We also show that the cosmic redshift, interpreted as an expansion effect, containts both the Doppler effect and the gravitational frequency shift., Comment: 18 pages, 2 figures. Revised version, accepted for publication in Am. J. Phys

Recently, there have been suggestions that the apparent accelerated expansion of the universe is not caused by repulsive gravitation due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this work, we investigate the behaviour of a dust dominated inhomogeneous Lemaitre-Tolman-Bondi universe model, and confront it with various astrophysical observations. We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bubble centered near the observer. With the additional assumption that the universe outside the bubble is approximately described by a homogeneous Einstein-de Sitter model, we find that the position of the first CMB peak can be made to match the WMAP observations. Whether or not it is possible to reproduce the entire CMB angular power spectrum in an inhomogeneous model without dark energy, is still an open question., Comment: 8 pages (REVTeX4), 4 figures. v2: Minor changes to text plus added some references. Accepted for publication in PRD

Recently, there has been suggestions that the apparent accelerated expansion of the universe is due not to a cosmological constant, but rather to inhomogeneities in the distribution of matter. In this work, we investigate a specific class of inhomogeneous models that can be solved analytically, namely the dust-dominated Lemaitre-Tolman-Bondi universe models. We show that they do not permit accelerated cosmic expansion., Comment: 9 pages, 1 figure. v3: Paper shortened and updated. References added. v4: Minor LATEX problem fixed. Submitted to JCAP

We look at a gas of dust and investigate how its entropy evolves with time under a spherically symmetric gravitational collapse. We treat the problem perturbatively and find that the classical thermodynamic entropy does actually increase to first order when one allows for gravitational potential energy to be transferred to thermal energy during the collapse. Thus, in this situation there is no need to resort to the introduction of an intrinsic gravitational entropy in order to satisfy the second law of thermodynamics., Comment: 9 pages, 4 figures. Major changes from previous version. We consider only thermodynamic entropy in this version. Published in PRD

We explore the recently introduced statefinder parameters. After reviewing their basic properties, we calculate the statefinder parameters for a variety of cosmological models, and investigate their usefulness as a means of theoretical classification of dark energy models. We then go on to consider their use in obtaining constraints on dark energy from present and future supernovae type Ia data sets. Provided that the statefinder parameters can be extracted unambiguously from the data, they give a good visual impression of where the correct model should lie. However, it is non-trivial to extract the statefinders from the data in a model-independent way, and one of our results indicates that an expansion of the dark energy density to second order in the redshift is inadequate. Hence, while a useful theoretical and visual tool, applying the statefinders to observations is not straightforward., Comment: v2, 14 pages, 18 figures. Added references, better figures. Submitted to A&A

We generalize Israel's formalism to cover singular shells embedded in a non-vacuum Universe. That is, we deduce the relativistic equation of motion for a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker spacetime. Also, we review the embedding of a Schwarzschild mass into a cosmological model using "curvature" coordinates and give solutions with (Sch/FLRW) and without the embedded mass (FLRW)., Comment: 25 pages, 2 figures

In this paper we review Penrose's Weyl curvature conjecture which states that the concept of gravitational entropy and the Weyl tensor is somehow linked, at least in a cosmological setting. We give a description of a certain entity constructed from the Weyl tensor, from the very early history of our universe until the present day. Inflation is an important mechanism in our early universe for homogenisation and isotropisation, and thus it must cause large effects upon the evolution of the gravitational entropy. Therefore the effects from inflationary fluids and a cosmological constant are studied in detail., Comment: 21 pages, 4 ps figures

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture., Comment: 20 pages, 7 ps figures

On the scales of galaxies and beyond there is evidence for unseen dark matter. In this paper we find the experimental limits to the density of dark matter bound in the solar system by studying its effect upon planetary motion., Comment: 9 pages, REVTeX, no figures

In four dimensions a Gauss-Bonnet term in the action corre- sponds to a total derivative, and it does not contribute to the classical equations of motion. For higher-dimensional geometries this term has the interesting property (shared with other dimensionally continued Euler densities) that when the action is varied with respect to the metric, it gives rise to a symmetric, covariantly conserved tensor of rank two which is a function of the metric and its first and second order derivatives. Here we review the unification of General Relativity and electromagnetism in the classical five-dimen- sional, restricted (with g_55 = 1) Kaluza-Klein model. Then we discuss the modifications of the Einstein-Maxwell theory that results from adding the Gauss-Bonnet term in the action. The resulting four-dimensional theory describes a non-linear U(1) gauge theory non-minimally coupled to gravity. For a point charge at rest, we find a perturbative solution for large distances which gives a mass-dependent correction to the Coulomb potential. Near the source we find a power-law solution which seems to cure the short-distance divergency of the Coulomb potential. Possible ways to obtain an experimen- tal upper limit to the coupling of the hypothetical Gauss- Bonnet term are also considered., Comment: 27 pages, compressed and uuencoded postscript file with unpacking instructions; major revision to section IV.D.2 on pages 15-16 ("Corrections to the Coulomb potential at short distances") and to the figure on page 27, revised unpacking instruction; to be published in The Annals of Physics (NY), NORDITA 94/50