scholarly journals SECOND ORDER FORMALISM IN POINCARÉ GAUGE THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 655-679 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Type Equation ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Field Equations ◽  
Tetrad Field ◽  
Yang Mills ◽  
Source Current

Changing the set of independent variables of Poincaré gauge theory and considering, in a manner similar to the second-order formalism of general relativity, the Riemannian part of the Lorentz connection as a function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case, the spin density playing the role of the source current in a Yang–Mills type equation for the torsion. The equivalence of the second-order and conventional first-order formalism is established and the corresponding Noether identities are discussed. Finally, a concrete Lagrangian is constructed and by means of a Yasskin-type ansatz, the field equations are reduced to a conventional Einstein–Proca system. Neglecting higher order terms in the spin-tensor, approximate solutions describing the exterior of a spin-polarized neutron star are presented and the possibility of the experimental detection of the torsion fields is briefly discussed.

scholarly journals A gauge-theoretic approach to gravity

2012 ◽  
Vol 468 (2144) ◽  
pp. 2129-2173 ◽  
Author(s):  
Kirill Krasnov
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Dynamical Theory ◽  
Uniqueness Theorems ◽  
Theoretic Approach ◽  
Field Equations ◽  
Yang Mills ◽  
Massless Spin ◽  
Invariant Gauge ◽  
Einstein’S General Relativity

Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.

Approximate solutions of the general relativity field equations with a scalar meson field

1963 ◽  
Vol 59 (4) ◽  
pp. 739-741 ◽  
Author(s):  
J. Hyde
Keyword(s):  
General Relativity ◽  
Scalar Meson ◽  
Empty Space ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Coordinate Transformations ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Image Position ◽  
Scalar Meson Field

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).

APPROXIMATE SOLUTIONS OF STATIONARY GAUGE STRINGS ON THE (r, z)-PLANE

1995 ◽  
Vol 04 (02) ◽  
pp. 267-277 ◽  
Author(s):  
R.J. SLAGTER
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Approximation Scheme ◽  
Analytic Solution ◽  
Approximate Solutions ◽  
Second Order ◽  
Singular Behavior ◽  
Axially Symmetric ◽  
Field Equations ◽  
Symmetric Spacetime

We derive a class of approximate solutions of the coupled Einstein-scalar-gauge field equations on an axially symmetric spacetime. An analytic solution of the resulting elliptic PDE’s can be obtained to any desired order by constructing the Riemann functions. As an example model, a solution is presented, which resembles the Nielsen-Olesen vortex close to the z=0 hyperplane. However, the solution shows some significant deviation from the classical vortex off the z=0 plane. The singular behavior, which one usually encounters in line-mass models, manifests itself through the second-order solutions in the approximation scheme. Further, in this “toy”-model, with sufficient angular momentum of the spinning string, gφφ becomes negative for some values of r.

scholarly journals Metric-Affine Gauge Theory of Gravity: I. Fundamental Structure and Field Equations

1997 ◽  
Vol 06 (03) ◽  
pp. 263-303 ◽  
Author(s):  
Frank Gronwald
Keyword(s):  
Gauge Theory ◽  
Reference Frames ◽  
Classical Field Theory ◽  
Classical Field ◽  
Affine Group ◽  
Field Equations ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Affine Gravity

We give a self-contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of tranlations is explained in detail.

Analytical study of the vibrating double-sided quintic nonlinear nano-torsional actuator using higher-order Hamiltonian approach

2021 ◽  
pp. 146134842110320
Author(s):  
Gamal Mohamed Ismail ◽  
Mahmoud Abul-Ez ◽  
Hijaz Ahmad ◽  
Nadia Mohamed Farea
Keyword(s):  
Analytical Study ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Hamiltonian Approach ◽  
Homotopy Perturbation ◽  
The Relationship ◽  
Better Than

In this work, we investigate and apply higher-order Hamiltonian approach (HA) as one of the novelty techniques to find out the approximate analytical solution for vibrating double-sided quintic nonlinear nano-torsional actuator. Periodic solutions are analytically verified, and consequently, the relationship between the initial amplitude and the natural frequency are obtained in a novel analytical way. The HA is then extended to the second-order to find more accurate results. To show the accuracy and applicability of the technique, the approximated results are compared with the homotopy perturbation method and numerical solution. According to the numerical results, it is highly remarkable that the second-order approximate solutions produce better than previously existing results and almost similar in comparing with the numerical solutions.

scholarly journals General Relativity with a Positive Cosmological Constant as a Gauge Theory.

2018 ◽  
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant

In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

Higher-order contributions to ion-acoustic solitary waves in a warm multicomponent plasma with an electron beam

2000 ◽  
Vol 63 (2) ◽  
pp. 139-155 ◽  
Author(s):  
W. M. MOSLEM
Keyword(s):  
Electron Beam ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Negative Ions ◽  
Type Equation ◽  
Higher Order ◽  
Second Order ◽  
Negative Ion ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

Higher-order contributions in reductive perturbation theory are studied for small- but finite-amplitude ion-acoustic solitary waves in a warm plasma with negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures and pressures). The basic set of fluid equations are reduced to a Korteweg–de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potential. At the critical negative-ion density, the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched coordinates is then used to derive a modified KdV equation and a linear inhomogeneous modified KdV-type equation at the critical density of negative ions for the second-order perturbed potential. Stationary solutions of the coupled equations, for both cases, are obtained using a renormalization method.

STRING FIELD THEORY

1987 ◽  
Vol 02 (01) ◽  
pp. 1-76 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gauge Theory ◽  
String Field Theory ◽  
Dimensional Space ◽  
Classical Solutions ◽  
Unified Field Theory ◽  
Superstring Theory ◽  
Yang Mills ◽  
Geometric Formulation

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU (N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory.

scholarly journals Compact objects in Horndeski gravity

2016 ◽  
Vol 25 (09) ◽  
pp. 1641006 ◽  
Author(s):  
Hector O. Silva ◽  
Andrea Maselli ◽  
Masato Minamitsuji ◽  
Emanuele Berti
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Neutron Stars ◽  
Recent Work ◽  
Second Order ◽  
Compact Objects ◽  
Degree Of Freedom ◽  
Field Equations ◽  
Special Position

Horndeski gravity holds a special position as the most general extension of Einstein’s theory of general relativity (GR) with a single scalar degree of freedom and second-order field equations. Because of these features, Horndeski gravity is an attractive phenomenological playground to investigate the consequences of modifications of GR in cosmology and astrophysics. We present a review of the progress made so far in the study of compact objects (black holes (BHs) and neutron stars (NSs)) within Horndeski gravity. In particular, we review our recent work on slowly rotating BHs and present some new results on slowly rotating NSs.

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