Localization of Gravity in Brane World with Arbitrary Extra Dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. We used the confining potential in this model to localized gravitons on the brane. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.     

Asymptotic Freedom in the Conformal Quantum Gravity with Matter

The grand unified theory (GUT) based on the O(N) and SU(N)-gauge groups after the conformally invariant gravity being included is investigated. We calculate the one-loop gravity contributions into the renormalization group equations and study their solutions. The analysis performed show that the asymptotic freedom behaviour early established for all GUT's coupling constants is not broken by taking into account this kind of gravity. However all restrictions imposed on the GUT multiplet composition become less firmly and the physical content of the constructed models is more realistic.     

Submillimeter Extra Dimensions and TeV-Scale Quantum Gravity

We briefly review some phenomenological, astrophysical, and cosmologicalaspects of theories with large extra dimensions and low-scale quantumgravity.     

Tunneling in Two Dimensions

Tunneling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials, [9]. The spatial domain is a two-dimensional square of side L with reflecting boundary conditions. For L large enough the penalty for tunneling from the minus to the plus equilibrium states is determined. Minimizing sequences are fully characterized and shown to have approximately a planar symmetry at all times, thus departing from the Wulff shape in the initial and final stages of the tunneling. In a final section (Sect. 11), we extend the results to d = 3 but their validity in d > 3 is still open.This research has been partially supported by MURST and NATO Grant PST.CLG.976552 and COFIN, Prin n.2004028108.     

Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discuss the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the model of gravity recently proposed by A. Saa 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 Planck 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.     

Spontaneous Compactification of Extra Dimensions in Eleven-Dimensional Quantum Gravity

The reduction of the eleven-dimensional pure gravity theory to a field theory to a field theory in the four-dimensional Minkowski space-time by means of the spontaneous compactification of the extra dimensions is investigated. The contribution of the quantum fluctuations of the eleven-dimensional second rank symmetric tensor field to the curvatures of the space-time and the compactified space of the extra dimensions are calculated in the one-loop approximations. It is shown that there exist the values of the cosmological constant such that the resulting four-dimensional theory is self-consistent.     

Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently, corrections to the standard Einstein-Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and ln R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory . On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.     

Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently, corrections to the standard Einstein-Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed： matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/ R gravity and In R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory. On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.     

A Numeric Solution for Einstein's Gravitational Theory with Proca Matter and Metric-Affine Gravity

A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordström type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity at its origin.     

Scalar Soliton in Newtonian Gravity Modelling Dark Matter Halos

Within standard Newtonian gravity, galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law. In particular, we show that a solvable toy model with a self-interaction U() borrowed from non-topological solitons produces already qualitatively correct rotation curves. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation.     

Isophasal Scattering Manifolds in Two Dimensions

We construct pairs of nonisometric, two-dimensional, asymptotically Euclidean manifolds X ₁ and X ₂ with the same scattering phase. Received: 25 August 2000 / Accepted: 1 June 2001     

On Matter and Metric in Affine Theory of Gravity

The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl.     

Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.     

Ostwald Ripening in Two Dimensions: Treatment with Pairwise Interactions

Ostwald ripening is the last stage of the evolution of a system with two coexisting phases. It is a relatively simple nonequilibrium phenomenon with several interesting features. For example, as the system coarsens it goes through a scaling state, one which looks the same (up to an overall length scale, which grows) at all times. The dynamics of the problem can be mapped, in two dimensions, onto an evolving Coulomb system. In this work we present a brief summary of a novel theoretical approach to this problem, based on an analytic derivation (using a mean-field approach) of an effective two-body interaction between droplets of the minority phase. The resulting interacting many-body dynamics is solved by a very efficient numerical algorithm, allowing us to follow the evolution of more than 10⁶ droplets on a simple workstation. The results are in excellent agreement with recent experiments.     

Sinh-Gordon Matter Field and a Solvable Model in Two-Dimensional Gravity

The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a sinh-Gordon matter field is investigated. We find that the classical equations of motion are exactly solvable, and analytically obtain the static solutions of induced metric and scalar curvature. These solutions have some new features and may be used to describe the naked singularities at the horizons.     

Compactification of Two Dimensions in General Relativity

Motivated by Kaluza-Klein theory and modern string theories, the class of exact solutions yielding product manifolds M ₂ × S ² in general relativity is investigated. The compact submanifold homeomorphic to S ² is chosen to be a very small sphere. Choosing an anisotropic fluid as the particular physical model, it is proved that very large mass density and tension provide the mechanism of compactification. In case the transverse pressure is chosen to be zero, the corresponding spacetime is homeomorphic to ² × S ², and thus provides a tractable non-flat metric. In this simple metric, the geodesic equations are completely solved, yielding motions of massive test particles. Next, the corresponding wave mechanics (given by the Klein-Gordon equation) is explored in the same curved background. A general class of exact solutions is obtained. Four conserved quantities are explicitly computed. The scalar particles exhibit a discrete mass spectrum.     

The Atomic Hydrogen in Two Spatial Dimensions

We resolve the problem of atomic hydrogen in two spatial dimensions exactly. Its spectrum ia different from that in three dimensions, M the angular momentum is not quantised in integer or half of odd-integer. We a h calculate the ground state energies for different cases of the parameter α, which may be related to the statistics of the electron in the atom.     

A Proof of Crystallization in Two Dimensions

Many materials have a crystalline phase at low temperatures. The simplest example where this fundamental phenomenon can be studied are pair interaction energies of the type where y(x) ∈ℝ² is the position of particle x and V(r) ∈ ℝ is the pair-interaction energy of two particles which are placed at distance r. Due to the Mermin-Wagner theorem it can't be expected that at finite temperature this system exhibits long-range ordering. We focus on the zero temperature case and show rigorously that under suitable assumptions on the potential V which are compatible with the growth behavior of the Lennard-Jones potential the ground state energy per particle converges to an explicit constant E_*: where E_* ∈ ℝ is the minimum of a simple function on [0,∞). Furthermore, if suitable Dirichlet- or periodic boundary conditions are used, then the minimizers form a triangular lattice. To the best knowledge of the author this is the first result in the literature where periodicity of ground states is established for a physically relevant model which is invariant under the Euclidean symmetry group consisting of rotations and translations.     

Large Bipolarons in Two and Three Dimensions

The large bipolaron in two and three dimensions is investigated by combining the reasonable asymptotic relative wavefunctions and the Lee-Low-Pines-Huybrechts (LLP-H) variational method. The values of the critical coupling constant α_C above which bipolarons may exist and the critical ratio of dielectric constants η_c below which bipolarons may exist are evaluated, which are very close to the recent results obtained within totally different variational approaches. It is also found that low-dimensional materials are more favorable for the formation of bipolarons.     

Status of the Asymptotic Safety Paradigm for Quantum Gravity and Matter

In the asymptotic safety paradigm, a quantum field theory reaches a regime with quantum scale invariance in the ultraviolet, which is described by an interacting fixed point of the Renormalization Group. Compelling hints for the viability of asymptotic safety in quantum gravity exist, mainly obtained from applications of the functional Renormalization Group. The impact of asymptotically safe quantum fluctuations of gravity at and beyond the Planck scale could at the same time induce an ultraviolet completion for the Standard Model of particle physics with high predictive power.