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Showing papers on "Four-force published in 2011"


Book
11 Jul 2011
TL;DR: In this article, the authors introduce Semi-Riemannian and Lorenz geometries for manifold theory, including Lie groups and Covering Manifolds, as well as the Calculus of Variations.
Abstract: Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorenz Geometry. Special Relativity. Constructions. Symmetry and Constant Curvature. Isometries. Calculus of Variations. Homogeneous and Symmetric Spaces. General Relativity. Cosmology. Schwarzschild Geometry. Causality in Lorentz Manifolds. Fundamental Groups and Covering Manifolds. Lie Groups. Newtonian Gravitation.

3,593 citations


Journal ArticleDOI
TL;DR: In this article, the relation between teleparallelism and local Lorentz invariance was analyzed and it was shown that generic modifications of the tele-parallel equivalent to general relativity will not respect local LRS.
Abstract: We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.

316 citations


Book
26 Sep 2011
TL;DR: Relativity in IAU Resolutions as mentioned in this paper is a special case of General Relativity and Relativistic Reference Frames 5 Post-Newtonian Coordinate Transformations (RNCT).
Abstract: 1 Newtonian celestial mechanics 2 Introduction to Special Relativity 3 General Relativity 4 Relativistic Reference Frames 5 Post-Newtonian Coordinate Transformations 6 Relativistic Celestial Mechanics 7 Relativistic Astrometry 8 Relativistic Geodesy 9 Relativity in IAU Resolutions

196 citations


Book
17 Jun 2011
TL;DR: A comprehensive survey of the development of the theory of scale relativity and fractal space-time can be found in this paper, where the fundamental laws of physics may be given a general form that unifies and thus goes beyond the classical and quantum regimes taken separately.
Abstract: This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies and thus goes beyond the classical and quantum regimes taken separately. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.

192 citations



Book
02 Oct 2011
TL;DR: In this paper, the authors present the special theory of relativity from a mathematical point of view, and discuss the kinematics of Special Relativity in terms of Lorentz transformations.
Abstract: Based on a course taught at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms for Minkowski space-time, and discusses the kinematics of Special Relativity in terms of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of the spinor space can induce a proper Lorentz mapping on the Minkowski space. Relativistic mechanics is discussed from a Lagrangian point of view, and the book concludes with a development of relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, and Dirac fields. The final chapter describes recent work on classical fields in an eight-dimensional covariant phase space.

45 citations


Journal ArticleDOI
TL;DR: In this article, an operationally-motivated local reference frame was proposed for a simple description of the rotation of polarization in an external gravitational field, and a solution of null geodesics in Kerr space-time that is organized around a new expansion parameter was presented.
Abstract: Rotation of polarization in an external gravitational field is one of the effects of general relativity that can serve as a basis for its precision tests A careful analysis of reference frames is crucial for a proper evaluation of this effect We introduce an operationally-motivated local reference frame that allows for a particularly simple description We present a solution of null geodesics in Kerr space-time that is organized around a new expansion parameter, allowing a better control of the series, and use it to calculate the resulting polarization rotation While this rotation depends on the reference-frame convention, we demonstrate a gauge-independent geometric phase for closed paths in general space-times

35 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle, and they give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-called Doubly special Relativity theories.
Abstract: Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality [G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, arXiv:1101.0931.] has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-called Doubly Special Relativity theories.

31 citations


Journal ArticleDOI
TL;DR: In this paper, a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity is derived, which involves several fields and a connection, but no spacetime metric at the fundamental level.
Abstract: We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of Newtonian gravity. It involves several fields and a connection, but no spacetime metric at the fundamental level. We show that the usual coordinate-dependent equations of post-Newtonian gravity are recovered when one specializes to asymptotically flat spacetimes and to appropriate classes of coordinates.

29 citations


Journal ArticleDOI
TL;DR: In this paper, Born's reciprocal general relativity theory in curved space-time was extended to the curved phase-space scenario, which requires the introduction of a complex Hermitian metric, torsion and nonmetricity.
Abstract: We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space–time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space–time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario.

29 citations


Journal ArticleDOI
TL;DR: In this paper, Trace Dynamics is used to construct a non-commutative relativistic special relativity, and a line-element is defined using the Trace over space-time coordinates which are assumed to be operators.

Journal ArticleDOI
TL;DR: This paper provided an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to fit higher level students.
Abstract: The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.

Posted Content
TL;DR: In this article, a well defined lattice-regularized theory for quantum gravity was proposed, which is invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms.
Abstract: Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To that end we need to present the tetrad by a composite field built as a bilinear combination of fermion fields. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms. Being well defined for large and fast varying fields at the ultraviolet cutoff, the theory simultaneously has chances of reproducing standard General Relativity in the infrared continuum limit. The present regularization of quantum gravity opens new possibilities of its unification with the Standard Model.


Journal ArticleDOI
TL;DR: In this paper, the authors summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it, and present solutions to the problems they identified.
Abstract: In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.

Journal ArticleDOI
TL;DR: In this paper, Tiwari et al. model electron as a spherically symmetric charged perfect fluid distribution of matter and extend the existing model by assuming a matter source characterized by quadratic equation of state in the context of general theory of relativity.
Abstract: Motivated by earlier studies (Tiwari et al. in Astrophys. Space Sci. 182:105, 1984; Herrera and Varela in Phys. Lett. 189:11, 1994), we model electron as a spherically symmetric charged perfect fluid distribution of matter. The existing model is extended assuming a matter source that is characterized by quadratic equation of state in the context of general theory of relativity. For the suitable choices of the parameters, our charged fluid models almost satisfy the physical properties of electron.

Book
10 Oct 2011
TL;DR: A Brief History of Relativity, Light, and Gravity as discussed by the authors The origins of Mass Relativity of Thermodynamics The 'General' Theory Short-Circuited Relativity in Hyperbolic Space Nonequivalence of Gravitation and Acceleration Aberration and Radiation Pressure in the Klein and Poincare Models The Inertia of Polarization
Abstract: A Brief History of Relativity, Light, and Gravity Which Geometry? The Origins of Mass Relativity of Thermodynamics The 'General' Theory Short-Circuited Relativity of Hyperbolic Space Nonequivalence of Gravitation and Acceleration Aberration and Radiation Pressure in the Klein and Poincare Models The Inertia of Polarization.

Proceedings ArticleDOI
TL;DR: In this paper, an alternative velocity addition scheme is proposed consistent with the invariance of the speed of light and the relativity of inertial frames, which is based on a transformation of a hyperbolic scator algebra.
Abstract: The reciprocity principle requests that if an observer, say in the laboratory, sees an event with a given velocity, another observer at rest with the event must see the laboratory observer with minus the same velocity. The composition of velocities in the Lorentz-Einstein scheme does not fulfill the reciprocity principle because the composition rule is neither commutative nor associative. In other words, the composition of two non-collinear Lorentz boosts cannot be expressed as a single Lorentz boost but requires in addition a rotation. The Thomas precession is a consequence of this composition procedure. Different proposals such as gyro-groups have been made to fulfill the reciprocity principle. An alternative velocity addition scheme is proposed consistent with the invariance of the speed of light and the relativity of inertial frames. An important feature of the present proposal is that the addition of velocities is commutative and associative. The velocity reciprocity principle is then immediately fulfilled. This representation is based on a transformation of a hyperbolic scator algebra. The proposed rules become identical with the special relativity addition of velocities in one dimension. They also reduce to the Galilean transformations in the low velocity limit. The Thomas gyration needs to be revised in this nonlinear realization of the special relativity postulates. The deformed Minkowski metric presented here is compared with other deformed relativity representations.

Journal ArticleDOI
TL;DR: In this article, the authors study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the travelling observer and an observer at rest, and show that the relationship between the proper times of different observers and the propagation of light signals between them, and use of compactification to describe the global structure of a relativistic model.
Abstract: The 'twin paradox' of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the travelling observer and an observer at rest. This paper is intended to give graduate students who are familiar with special relativity and have some basic experience of general relativity a deeper insight into accelerated motion in general relativity, into the relationship between the proper times of different observers and the propagation of light signals between them, and into the use of compactification to describe the global structure of a relativistic model.


Journal ArticleDOI
TL;DR: In this paper, different forms of the Hamiltonian formulations of linearized General Relativity/spin-2 theories are discussed in order to show their similarities and differences, and it is demonstrated that non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary.
Abstract: The different forms of the Hamiltonian formulations of linearized General Relativity/spin-2 theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary. The Hamiltonians and the constraints are different in these two formulations but the structure of the constraint algebra and the gauge invariance derived from it are the same. It is shown that these equivalent Hamiltonian formulations are related to each other by a canonical transformation, which is explicitly given. The relevance of these results to the full theory of General Relativity is briefly discussed.

01 Jul 2011
TL;DR: In this article, the authors present three different projects, all of which are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well.
Abstract: This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link between the highly damped modes and black hole thermodynamics. The third chapter is related to the topic of multiplication of tensorial distributions.


Posted Content
TL;DR: The aim of this paper is to develop a precise language in order to provide a precise formulation of the special relativity principle, which is considered as a universal meta-law, which must be valid for all physical laws in all situations.
Abstract: The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality.


Book ChapterDOI
24 Jun 2011

Journal ArticleDOI
M. H. M. Hilo1
TL;DR: In this article, a new method to prove the equation of the gravitational red shift of spectral lines was presented, which is based on the generalized special relativity (GSR) theory.
Abstract: In this work we present a study of a new method to prove the equation of the gravitational red shift of spec-tral lines. That’s according to the generalized special relativity theory. The equation of the gravitational red shift of spectral lines has been studied in many different works, using different methods depending on the Newtonian mechanics, and other theories. Although attention was drawn to the fact that the well-known ex-pression of the gravitational Red-Shift of spectral lines may be derived with no recourse to the general rela-tivity theory! In this study a unique derivation has been done using the Generalized Special Relativity (GSR) and the same result obtained.

Journal ArticleDOI
01 Feb 2011
TL;DR: In this article, the authors consider Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions.
Abstract: We consider Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, in the era when the energy density of the scalar potential dominates over the energy density of ordinary matter. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible solutions. We argue that the topology of phase trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor. To the classes of models which asymptotically approach general relativity we give the solutions also in cosmological time and conclude with some observational implications.