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

Weighing the Milky Way

We describe an experiment to measure the mass of the Milky Way galaxy. The experiment is based on calculated light travel times along orthogonal directions in the Schwarzschild metric of the Galactic center. We show that the difference is proportional to the Galactic mass. We apply the result to light travel times in a 10cm Michelson type interferometer located on Earth. The mass of the Galactic center is shown to contribute 10^-6 to the flat space component of the metric. An experiment is proposed to measure the effect.Comment: 10 pages, 1 figur

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

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

No-go theorem for false vacuum black holes

We study the possibility of non-singular black hole solutions in the theory of general relativity coupled to a non-linear scalar field with a positive potential possessing two minima: a `false vacuum' with positive energy and a `true vacuum' with zero energy. Assuming that the scalar field starts at the false vacuum at the origin and comes to the true vacuum at spatial infinity, we prove a no-go theorem by extending a no-hair theorem to the black hole interior: no smooth solutions exist which interpolate between the local de Sitter solution near the origin and the asymptotic Schwarzschild solution through a regular event horizon or several horizons.Comment: 16 pages, 1 figure, Latex, some references added, to appear in Classical and Quantum Gravit

Gradient expansion(s) and dark energy

Motivated by recent claims stating that the acceleration of the present Universe is due to fluctuations with wavelength larger than the Hubble radius, we present a general analysis of various perturbative solutions of fully inhomogeneous Einstein equations supplemented by a perfect fluid. The equivalence of formally different gradient expansions is demonstrated. If the barotropic index vanishes, the deceleration parameter is always positive semi-definite.Comment: 17 pages, no figure

Inflationary Cosmologies in an Anisotropic Brane World

A new cosmological solution of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and with perfect fluid as matter sources is presented. The matter is described by a scalar field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario, in the first case universe evolves from singularity and in the second case universe expands without singularity.Comment: 15 pages, no figures, LaTe

k-Essence, superluminal propagation, causality and emergent geometry

The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.Comment: 34 pages, 5 figure

Cosmic Acceleration Driven by Mirage Inhomogeneities

A cosmological model based on an inhomogeneous D3-brane moving in an AdS_5 X S_5 bulk is introduced. Although there is no special points in the bulk, the brane Universe has a center and is isotropic around it. The model has an accelerating expansion and its effective cosmological constant is inversely proportional to the distance from the center, giving a possible geometrical origin for the smallness of a present-day cosmological constant. Besides, if our model is considered as an alternative of early time acceleration, it is shown that the early stage accelerating phase ends in a dust dominated FRW homogeneous Universe. Mirage-driven acceleration thus provides a dark matter component for the brane Universe final state. We finally show that the model fulfills the current constraints on inhomogeneities.Comment: 14 pages, 1 figure, IOP style. v2, changed style, minor corrections, references added, version accepted in Class. Quant. Gra