Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.Comment: 6 pages, no figures, Revtex4. Some discussions on the physical nature of the interior solution and on the omega->infinity limit and some references added. Version to appear in Phys. Rev.

Intrinsic Geometry of a Null Hypersurface

We apply Cartan's method of equivalence to construct invariants of a given null hypersurface in a Lorentzian space-time. This enables us to fully classify the internal geometry of such surfaces and hence solve the local equivalence problem for null hypersurface structures in 4-dimensional Lorentzian space-times

Modelling the rotational curves of spiral galaxies with a scalar field

In a previous work (Mbelek 2001), we modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion of the stars the dynamical terms from an external real self-interacting scalar field, $\psi$, minimally coupled to gravity and which respects the equivalence principle in the weak fields and low velocity approximation. This model appeared to have three free parameters : the turnover radius, $r_{0}$, the maximum tangential velocity, $v_{\theta max} = v_{\theta}(r_{0})$, plus a strictly positive integer, $n$. Here, we propose a new improved version where the coupling of the $\psi$-field to dark matter is emphasized at the expense of its self-interaction. This reformulation presents the very advantageous possibility that the same potential is used for all galaxies. Using at the same time a quasi-isothermal dark matter density and the scalar field helps to better fit the RC of spiral galaxies. In addition, new correlations are established.Comment: Latex, 5 pages with 3 Postscript figure

Extended Inflation with an Exponential Potential

In this paper we investigate extended inflation with an exponential potential $V(\sigma)= V_0 e^{-\kappa\sigma}$, which provides a simple cosmological scenario where the distribution of the constants of Nature is mostly determined by $\kappa$. In particular, we show that this theory predicts a uniform distribution for the Planck mass at the end of inflation, for the entire ensemble of universes that undergo stochastic inflation. Eternal inflation takes place in this scenario for a broad family of initial conditions, all of which lead up to the same value of the Planck mass at the end of inflation. The predicted value of the Planck mass is consistent with the observed value within a comfortable range of values of the parameters involved.Comment: 6 pages, 2 figure

General Relativity as an Attractor in Scalar-Tensor Stochastic Inflation

Quantum fluctuations of scalar fields during inflation could determine the very large-scale structure of the universe. In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants like the Planck mass and the effective Brans--Dicke parameter, $\omega$. In the particular case of Brans--Dicke gravity, where $\omega$ is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a theory with variable $\omega$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $\omega$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.Comment: LaTeX (with RevTex) 11 pages, 2 uuencoded figures appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm

Extended Gravity Theories and the Einstein-Hilbert Action

I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and $n$ further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and extent of the conformal equivalence between extended gravity theories and general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-

Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Plank "constant" is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.Comment: 29 pages, latex, no figures. New Section on semiclassical limit of wave equation added; old references rearranged; new references, remarks, comments, and acknowledgments added; typos correcte

Nielsen-Olesen vortex in varying-alpha theories

We consider soliton solutions to Bekenstein's theory, for which the fine structure constant $\alpha=e^2/(4\pi\hbar c)$ is allowed to vary due to the presence of a dielectric field pervading the vacuum. More specifically we investigate the effects of a varying $\alpha$ upon a complex scalar field with a U(1) electromagnetic gauge symmetry subject to spontaneous symmetry breaking. We find vortex solutions to this theory, similar to the Nielsen-Olesen vortex. Near the vortex core the electric charge is typically much larger than far away from the string, lending these strings a superconducting flavour. In general the dielectric field coats the usual local string with a global string envelope. We discuss the cosmological implications of networks of such strings, with particular emphasis on their ability to generate inhomogeneous recombination scenarios. We also consider the possibility of the dielectric being a charged free field. Even though the vacuum of such a field is trivial, we find that the dielectric arranges itself in the shape of a local string, with a quantized magnetic flux at the core -- presumably borrowing these topological features from the underlying Nielsen-Olesen vortex.Comment: 7 pages, 1 figur

Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehne

Black holes in the Brans-Dicke-Maxwell theory

The black hole solutions in the higher dimensional Brans-Dicke-Maxwell theory are investigated. We find that the presence of the nontrivial scalar field depends on the spacetime dimensions (D). When D=4, the solution corresponds to the Reissner-Nordstr\"{o}m black hole with a constant scalar field. In higher dimensions (D>4), one finds the charged black hole solutions with the nontrivial scalar field. The thermal properties of the charged black holes are discussed and the reason why the nontrivial scalar field exists are explained. Also the solutions for higher dimensional Brans-Dicke theory are given for comparison.Comment: Revtex, 5 pages, no figures, contents were rewritten and new references were adde