scholarly journals A PERTURBATION APPROACH TO TRANSLATIONAL GRAVITY

2013 ◽  
Vol 10 (10) ◽  
pp. 1350062
Author(s):  
J. JULVE ◽  
A. TIEMBLO
Keyword(s):  
Gravitational Constant ◽  
General Structure ◽  
Isotropic Case ◽  
Perturbation Approach ◽  
Nonlinear Realization ◽  
Metric Tensor ◽  
First Order ◽  
Group Of Isometries ◽  
Natural Expansion ◽  
Gauge Formulation

Within a gauge formulation of 3+1 gravity relying on a nonlinear realization of the group of isometries of space-time, a natural expansion of the metric tensor arises and a simple choice of the gravity dynamical variables is possible. We show that the expansion parameter can be identified with the gravitational constant and that the first-order depends only on a diagonal matrix in the ensuing perturbation approach. The explicit first-order solution is calculated in the static isotropic case, and its general structure is worked out in the harmonic gauge.

scholarly journals DYNAMICAL VARIABLES IN GAUGE-TRANSLATIONAL GRAVITY

2011 ◽  
Vol 08 (02) ◽  
pp. 381-393 ◽  
Author(s):  
J. JULVE ◽  
A. TIEMBLO
Keyword(s):  
Gauge Theory ◽  
Symmetric Space ◽  
Gravity Field ◽  
Gauge Group ◽  
First Principles ◽  
General Structure ◽  
Diagonal Matrix ◽  
Nonlinear Realization ◽  
First Order ◽  
Group Of Isometries

Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first principles we verify that a nonlinear realization of the symmetry provides the general structure of this gauge theory, leading to a simple choice of dynamical variables of the gravity field corresponding, at first-order, to a diagonal matrix, whereas the non-diagonal elements contribute only to higher orders.

Nonlinear self-phase-modulation effects: a vectorial first-order perturbation approach

1995 ◽  
Vol 20 (5) ◽  
pp. 456 ◽  
Author(s):  
Velko P. Tzolov ◽  
Nicolas Godbout ◽  
Suzanne Lacroix ◽  
Marie Fontaine
Keyword(s):  
Phase Modulation ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
Self Phase Modulation ◽  
First Order ◽  
First Order Perturbation

Spherical indentation of an elastic bilayer: A modification of the perturbation approach

2008 ◽  
Vol 23 (11) ◽  
pp. 2935-2943 ◽  
Author(s):  
Jae Hun Kim ◽  
Chad S. Korach ◽  
Andrew Gouldstone
Keyword(s):  
Analytic Solution ◽  
Effective Modulus ◽  
Spherical Indentation ◽  
Perturbation Approach ◽  
Instrumented Indentation ◽  
Flat Punch ◽  
First Order ◽  
Property Measurement ◽  
Film Substrate ◽  
Contact Size

Accurate mechanical property measurement of films on substrates by instrumented indentation requires a solution describing the effective modulus of the film/substrate system. Here, a first-order elastic perturbation solution for spherical punch indentation on a film/substrate system is presented. Finite element method (FEM) simulations were conducted for comparison with the analytic solution. FEM results indicate that the new solution is valid for a practical range of modulus mismatch, especially for a stiff film on a compliant substrate. It also shows that effective modulus curves for the spherical punch deviates from those of the flat punch when the thickness is comparable to contact size.

Almost strongly minimal theories. I

1972 ◽  
Vol 37 (3) ◽  
pp. 487-493 ◽  
Author(s):  
John T. Baldwin
Keyword(s):  
Algebraic Closure ◽  
Natural Extension ◽  
Stone Space ◽  
First Order ◽  
Order Language ◽  
Simple Class ◽  
The Universe ◽  
Natural Expansion ◽  
Minimal Formula

In [1] the notions of strongly minimal formula and algebraic closure were applied to the study of ℵ1-categorical theories. In this paper we study a particularly simple class of ℵ1-categorical theories. We characterize this class in terms of the analysis of the Stone space of models of T given by Morley [3].We assume familiarity with [1] and [3], but for convenience we list the principal results and definitions from those papers which are used here. Our notation is the same as in [1] with the following exceptions.We deal with a countable first order language L. We may extend the language L in several ways. If is an L-structure, there is a natural extension of L obtained by adjoining to L a constant a for each (the universe of ). For each sentence A(a1, …, an) ∈ L(A) we say satisfies A(a1, …, an) and write if in Shoenfield's notation If is an L-structure and X is a subset of , then L(X) is the language obtained by adjoining to L a name x for each is the natural expansion of to an L(X)-structure. A structure is an inessential expansion [4, p. 141] of an L-structure if for some .

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

scholarly journals ON THE QUASI-ISOTROPIC INFLATIONARY SOLUTION

2003 ◽  
Vol 12 (10) ◽  
pp. 1845-1857 ◽  
Author(s):  
GIOVANNI IMPONENTE ◽  
GIOVANNI MONTANI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Small Function ◽  
Inflationary Universe ◽  
Arbitrary Form ◽  
Metric Tensor ◽  
Dominant Term ◽  
First Order ◽  
Effective Cosmological Constant ◽  
Relativistic Matter

In this paper we find a solution for a quasi-isotropic inflationary Universe which allows to introduce in the problem a certain degree of inhomogeneity. We consider a model which generalizes the (flat) FLRW one by introducing a first order inhomogeneous term, whose dynamics is induced by an effective cosmological constant. The 3-metric tensor is constituted by a dominant term, corresponding to an isotropic-like component, while the amplitude of the first order one is controlled by a "small" function η(t). In a Universe filled with ultra relativistic matter and a real self-interacting scalar field, we discuss the resulting dynamics, up to first order in η, when the scalar field performs a slow roll on a plateau of a symmetry breaking configuration and induces an effective cosmological constant. We show how the spatial distribution of the ultra relativistic matter and of the scalar field admits an arbitrary form but nevertheless, due to the required inflationary e-folding, it cannot play a serious dynamical role in tracing the process of structures formation (via the Harrison–Zeldovic spectrum). As a consequence, this paper reinforces the idea that the inflationary scenario is incompatible with a classical origin of the large scale structures.

Vector-tensor field theories and the Einstein-Maxwell field equations

1974 ◽  
Vol 341 (1626) ◽  
pp. 285-297 ◽  
Keyword(s):  
Dimensional Space ◽  
Field Theories ◽  
Maxwell Field ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lagrange Equations ◽  
Third Order ◽  
Metric Tensor ◽  
First Order ◽  
First Derivative

The Euler-Lagrange equations corresponding to a Lagrange density which is a function of the metric tensor g ij and its first two derivatives together with the first derivative of a vector field ψ i are investigated. In general, the Euler-Lagrange equations obtained by variation of g ij are of fourth order in g ij and third order in ψ i . It is shown that in a four dimensional space the only Euler-Lagrange equations which are of second order in g ij and first order in ψ i are the Einstein field equations (with an energy-momentum term). Various conditions are obtained under which the Einstein-Maxwell field equations are then an inevitable consequence.

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