Modification of the Coulomb potential from a Kaluza-Klein model with a Gauss-Bonnet term in the action

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 94/5

The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.Comment: 16 page

Maximum Mass-Radius Ratios for Charged Compact General Relativistic Objects

Upper limits for the mass-radius ratio and total charge are derived for stable charged general relativistic matter distributions. For charged compact objects the mass-radius ratio exceeds the value 4/9 corresponding to neutral stars. General restrictions for the redshift and total energy (including the gravitational contribution) are also obtained.Comment: 6 pages, 2 figures, RevTex. To appear in Europhys. Let

Bounds on the basic physical parameters for anisotropic compact general relativistic objects

We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant. The values of these quantities are strongly dependent on the value of the anisotropy parameter (the difference between the tangential and radial pressure) at the surface of the star. In the presence of the cosmological constant, a minimum mass configuration with given anisotropy does exist. Anisotropic compact stellar type objects can be much more compact than the isotropic ones, and their radii may be close to their corresponding Schwarzschild radii. Upper bounds for the anisotropy parameter are also obtained from the analysis of the curvature invariants. General restrictions for the redshift and the total energy (including the gravitational contribution) for anisotropic stars are obtained in terms of the anisotropy parameter. Values of the surface redshift parameter greater than two could be the main observational signature for anisotropic stellar type objects.Comment: 18 pages, no figures, accepted for publication in CQ

Causality-Violating Higgs Singlets at the LHC

We construct a simple class of compactified five-dimensional metrics which admits closed timelike curves (CTCs), and derive the resulting CTCs as analytic solutions to the geodesic equations of motion. The associated Einstein tensor satisfies all the null, weak, strong and dominant energy conditions. In particular, no negative-energy "tachyonic" matter is required. In extra-dimensional models where gauge charges are bound to our brane, it is the Kaluza-Klein (KK) modes of gauge-singlets that may travel through the CTCs. From our brane point of view, many of these KK modes would appear to travel backward in time. We give a simple model in which time-traveling Higgs singlets can be produced by the LHC, either from decay of the Standard Model (SM) Higgs or through mixing with the SM Higgs. The signature of these time-traveling singlets is a secondary decay vertex pre-appearing before the primary vertex which produced them. The two vertices are correlated by momentum conservation. We demonstrate that pre-appearing vertices in the Higgs singlet-doublet mixing model may well be observable at the LHC.Comment: 55 pages, 5 figures, v4: Version updated to include in single manuscript the contents of Erratum [Phys. Rev. D 88, 069901(E) (2013)], Reply [Phys. Rev. D 88, 068702 (2013)], Comment [Phys. Rev. D 88, 068701 (2013), arXiv:1302.1711], and original published article [Phys. Rev. D 87, 045004 (2013), arXiv:1103.1373]. Positive conclusions remain unchange

Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models

A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with the time is also discussed.Comment: 23 pages, accepted in PR

Minimum mass-radius ratio for charged gravitational objects

We rigorously prove that for compact charged general relativistic objects there is a lower bound for the mass-radius ratio. This result follows from the same Buchdahl type inequality for charged objects, which has been extensively used for the proof of the existence of an upper bound for the mass-radius ratio. The effect of the vacuum energy (a cosmological constant) on the minimum mass is also taken into account. Several bounds on the total charge, mass and the vacuum energy for compact charged objects are obtained from the study of the Ricci scalar invariants. The total energy (including the gravitational one) and the stability of the objects with minimum mass-radius ratio is also considered, leading to a representation of the mass and radius of the charged objects with minimum mass-radius ratio in terms of the charge and vacuum energy only.Comment: 19 pages, accepted by GRG, references corrected and adde

Self-forces in the Spacetime of Multiple Cosmic Strings

We calculate the electromagnetic self-force on a stationary linear distribution of four-current in the spacetime of multiple cosmic strings. It is shown that if the current is infinitely thin and stretched along a line which is parallel to the strings the problem admits an explicit solution.Comment: This paper has been produced in Latex format and has 18 page