Showing papers on "Four-force published in 2010"

Republication of: New mechanics of material systems

Abstract: This is an English translation of the second of two papers by Myron Mathisson, first published in German in 1931 and 1937, in which he presented the correct formulation of equations of motion of spinning bodies in general relativity (today known as the Mathisson–Papapetrou equations) The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal This republication is accompanied by an editorial note and Mathisson’s brief biography, both written by Andrzej Trautman

Conformal equivalence in classical gravity: the example of "veiled" General Relativity

Abstract: In the theory of General Relativity, gravity is described by a metric which couples minimally to the fields representing matter We consider here its "veiled" versions where the metric is conformally related to the original one and hence is no longer minimally coupled to the matter variables We show on simple examples that observational predictions are nonetheless exactly the same as in General Relativity, with the interpretation of this "Weyl" rescaling "a la Dicke", that is, as a spacetime dependence of the inertial mass of the matter constituents

On the consistency of the Horava Theory

Abstract: With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Horava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant lambda. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of lambda deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.

Scalar-tensor cosmologies with a potential in the general relativity limit: Phase space view

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. We focus upon the phase space of the scalar field. 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 phase portraits. We argue that the topology of 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.

An introduction to relativity

Abstract: 1. The special theory of relativity 2. From special to the general theory of relativity 3. Vectors and tensors 4. Covariant differentiation 5. Curvature of spacetime 6. Spacetime symmetries 7. Physics in curved spacetime 8. Einstein's equations 9. The Schwarzschild solutions 10. Experimental tests of general relativity 11. Gravitational radiation 12. Relativistic astrophysics 13. Black holes 14. The expanding universe 15. Friedmann models 16. The early universe 17. Observational cosmology 18. Beyond relativity References Index.

Relativity, gravitation and cosmology

Abstract: 1. Special relativity and spacetime 2. Special relativity and physical laws 3. Geometry and curved spacetime 4. General relativity 5. The Schwarzschild solution and black holes 6. Testing general relativity 7. Cosmological solutions 8. Our Universe Index.

The principle of relativity, kinematics and algebraic relations

Abstract: Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.

First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers

Abstract: This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\'eka, Madar\'asz and N\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and general relativity; however, its main subject is the extension to accelerated observers (AccRel). One surprising result is that natural extension to accelerated observers is not enough if we want our theory to imply certain experimental facts, such as the twin paradox. Even if we add the whole first-order theory of real numbers to this natural extension, it is still not enough to imply the twin paradox. Nevertheless, that does not mean that this task cannot be carried out within first-order logic since by approximating a second-order logic axiom of real numbers, we introduce a first-order axiom schema that solves the problem. Our theory AccRel nicely fills the gap between special and general relativity theories, and only one natural generalization step is needed to achieve a first-order logic axiomatization of general relativity from it. We also show that AccRel is strong enough to make predictions about the gravitational effect slowing down time. Our general aims are to axiomatize relativity theories within pure first-order logic using simple, comprehensible and transparent basic assumptions (axioms); to prove the surprising predictions (theorems) of relativity theories from a few convincing axioms; to eliminate tacit assumptions from relativity by replacing them with explicit axioms formulated in first-order logic (in the spirit of the first-order logic foundation of mathematics and Tarski's axiomatization of geometry); and to investigate the relationship between the axioms and the theorems.

Construction of N-body initial data sets in general relativity

Abstract: Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions of each of the N given solutions. This generalizes earlier work which handled the time-symmetric case, thus providing a construction of large classes of initial data for the many body problem in general relativity.

Averaging Spacetime: Where do we go from here?

Abstract: The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining a mathematically precise covariant averaging procedure for tensor fields over differentiable manifolds. Together, these two ideas have been called the averaging problem for General Relativity. In the first part of the talk, an attempt to review some the various approaches to this problem will be given, highlighting strengths, weaknesses, and commonalities between them. In the second part of the talk, an argument will be made, that if one wishes to develop a well-defined averaging procedure, one may choose to parallel transport along geodesics with respect to the Levi-Cevita connection or, use the Weitzenbock connection and ensure the transportation is independent of path. The talk concludes with some open questions to generate further discussion.

A First Course in General Relativity (Second Edition)

Abstract: A few years ago, in my review of Sean Carroll's book in Classical and Quantum Gravity [1], I wrote that while the 1970s was the decade of Weinberg [2] and Misner, Thorne and Wheeler [3], and while the eighties was the decade of Schutz [4] and Wald [5], the 2000s was clearly the decade of Hartle [6] and Carroll [7] In my opinion, these books continue to stand out in the surprisingly dense crowd of introductory textbooks on general relativity At the dawn of this new decade I look forward to see what fresh pedagogical insights will be produced next, and who will be revealed as the winners of the 2010s It is, of course, much too early to tell, but Schutz is back, and he will set the standard just as he did back in 1985 This is the long-awaited second edition of his `First Course', a short, accessible, and very successful introduction to general relativity The changes from the first edition are modest: Schutz wisely refrained from bloating the text with new topics, and limited himself to updating his discussion of gravitational-wave sources and detectors, neutron-star and black-hole astrophysics, and suggestions for further reading Most importantly, he completely rewrote the chapter on cosmology, a topic that has evolved enormously since the first edition The book begins in chapter 1 with a beautiful review of special relativity that emphasizes spacetime geometry and stays away from an algebraic approach based on the Lorentz transformation, which appears only later in the chapter This is followed up in chapters 2 and 3 with an introduction to vector and tensor analysis in flat spacetime The point of view is modern (tensors are defined as linear mapping of vectors and one-forms into real numbers) but the presentation is very accessible and avoids an overload of mathematical fine print In chapter 4 the book introduces the spacetime description of fluids; it is here that the energy?momentum tensor makes its first appearance The move to curved spacetime is tackled next In chapter 5 the principle of equivalence is used to motivate the notion that gravity is a manifestation of spacetime curvature Tensor calculus in curved spacetime is approached gently, by first working through a generalization to curvilinear coordinates A systematic introduction to differential geometry is provided in chapter 6; here the reader is initiated in Riemannian manifolds, covariant differentiation, parallel transport, geodesics, the curvature tensors, and the Bianchi identities This is a formidable chapter, but the student is guided by a sure hand, and the presentation is both beautiful and accessible The next two chapters bring differential geometry to physics In chapter 7 the reader learns how to formulate the laws of physics in a curved spacetime, and in chapter 8 the Einstein field equations are finally formulated The chapter ends with a thorough treatment of the weak-field limit in the Lorenz gauge The following chapters present applications of the theory Chapter 9 is devoted to gravitational waves: propagation, detection, generation, energy balance, and astrophysical sources Here, as always, the discussion is accessible and fully up-to-date I could identify one weakness, which I have noted in many other textbooks (this is a pet peeve of mine, which seems to be turning into an obsession): the quadrupole formula for the gravitational-wave field is derived on the basis of the linearized theory, without warning the reader that the derivation does not apply to self-gravitating systems This is, however, compensated by a major strength: Schutz's derivation of the energy carried off by gravitational waves is based on a beautiful physical argument that bypasses the construction of an energy?momentum tensor for the gravitational-wave field; the complexities associated with such a construction are well known, and it is nice to see that Schutz has found a nice way around In chapter 10 the exact theory is applied to stellar structure, and in chapter 11 the student is introduced to black holes A large part of the chapter is devoted to the study of geodesic motion in Schwarzschild spacetime, and this allows Schutz to make contact with the classical tests of general relativity: perihelion advance and light deflection The singular behaviour of the Schwarzschild coordinates at the event horizon is described in detail This reveals another weakness of the book: the Kruskal coordinates are simply written down, with no derivation and little motivation; it is a pity that Schutz did not choose to introduce the Eddington--Finkelstein coordinates, or the Painlev??Gullstand coordinates, as easier alternatives The chapter ends with a general discussion of black holes (including their place in astrophysics and a description of the Hawking effect) and a detailed presentation of the Kerr solution The last chapter (chapter 12) is devoted to cosmology, and this is the part of the book that was the most thoroughly revised The presentation begins with the enunciation of the cosmological principle and a derivation of the Friedmann?Lemaitre models It continues with a discussion of cosmological dynamics in the presence of pressureless matter, radiation, and a cosmological constant (of which nobody wanted to be reminded at the time of the first edition) It concludes with an up-to-date review of cosmological measurements and a (very) brief history of the Universe, from the big bang to inflation, to recombination, to structure formation The presentation of general relativity and its applications contained in this book is suitable for undergraduate students who would prefer the standard `math-first approach' to Hartle's `physics-first approach' The student will learn the essentials of differential geometry in a gentle way, and will then apply these tools to physics in curved spacetime; all of this can be accomplished in a brisk one-semester course The book leaves out many topics than can be found in more advanced texts, such as Lie differentiation, differential forms, Killing vectors, the more abstract formulation of differential geometry (in terms of charts and diffeomorphisms), and the Lagrangian formulation of general relativity This limitation of scope is wise: Schutz masterly covers the essentials in an efficient and small package, and relegates all refinements to further reading in other textbooks; this is a sound learning strategy To conclude I will state that I just love this book I love it today as much as I did when I first came across it as an undergraduate student The revisions bring the book up-to-date, and they ensure that Schutz's text will remain in the pantheon of introductory general relativity books for many years to come References [1] Poisson E 2005 Review of Spacetime and Geometry: An Introduction to General Relativity, by S M Carroll Class Quantum Grav 22 4385?4386 [2] Weinberg S 1972 Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York: Wiley) [3] Misner C W, Thorne K S, and Wheeler J A 1973 Gravitation (San Francisco, CA: Freeman) [4] Schutz B F 1985 A First Course in General Relativity (Cambridge: Cambridge University Press) [5] Wald R M 1984 General Relativity (Chicago : Chicago University Press) [6] Hartle J B 2003 Gravity: An Introduction to Einstein's General Relativity (San Francisco, CA: Addison-Wesley) [7] Carroll S 2003 Spacetime and Geometry: An Introduction to General Relativity (San Francisco, CA: Benjamin Cummings)

The Motion of a Body in Newtonian Theories

Abstract: A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation (often called Newton-Cartan theory). It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.

Deformed Special Relativity from Asymptotically Safe Gravity

Abstract: By studying the notion of a fundamentally minimal length scale in asymptotically safe gravity we find that a specific version of deformed special relativity (DSR) naturally arises in this approach. We then consider two thought experiments to examine the interpretation of the scenario and discuss similarities and differences to other approaches to DSR.

The robertson walker metric in a pseudo-complex general relativity

Abstract: We investigate the consequences of the pseudo-complex General Relativity within a pseudo-complexified Robertson–Walker metric. A contribution to the energy–momentum tensor arises, which corresponds to a dark energy and may change with the radius of the universe, i.e., time. Only when the Hubble function H does not change in time, the solution is consistent with a constant Λ.

Special relativity as a noncommutative geometry: Lessons for deformed special relativity

Abstract: Deformed special relativity (DSR) is obtained by imposing a maximal energy to special relativity and deforming the Lorentz symmetry (more exactly, the Poincar\'e symmetry) to accommodate this requirement. One can apply the same procedure in the context of Galilean relativity by imposing a maximal speed (the speed of light). Effectively, one deforms the Galilean group and this leads to a noncommutative space structure, together with the deformations of composition of speed and conservation of energy momentum. In doing so, one runs into most of the ambiguities that one stumbles onto in the DSR context. However, this time, special relativity is there to tell us what is the underlying physics, in such a way we can understand and interpret these ambiguities. We use these insights to comment on the physics of DSR.

On the running of the cosmological constant in quantum general relativity

Abstract: We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.

Notes on thermodynamics in special relativity

Abstract: Foundations of thermodynamics in special theory of relativity are considered. We argue that from the phenomenological point of view the correct relativistic transformations of heat and absolute temperature are given by the formulae proposed by H. Ott, H. Arzelies and C. M\oller. It is shown that the same transformation rules can be also found from the relativistic Gibbs distribution for ideal gas. This distribution has been recently verified by the computer simulations. Phenomenological and statistical thermometers in relativistic thermodynamics are analysed.

Does Quantum Nonlocality Irremediably Conflict with Special Relativity

Abstract: We reconsider the problem of the compatibility of quantum nonlocality and the requests for a relativistically invariant theoretical scheme. We begin by discussing a recent important paper by T. Norsen on this problem and we enlarge our considerations to give a general picture of the conceptually relevant issue to which this paper is devoted.

Quasilocal Hamiltonians in general relativity

Abstract: We analyze the definition of quasilocal energy in general relativity based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular, the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasilocal energy in general relativity requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.

Comments on Nonlocality in Deformed Special Relativity, in reply to arXiv:1004.0664 by Lee Smolin and arXiv:1004.0575 by Jacob et al

Abstract: It was previously shown that models with deformations of special relativity that have an energy-dependent yet observer-independent speed of light suffer from nonlocal effects that are in conflict with observation to very high precision. In a recent paper it has been proposed that these paradoxa arise only in the classical limit and can be prevented by an ad-hoc introduction of a quantum uncertainty that would serve to hide the nonlocality. We will show here that the proposed ansatz for this resolution is inconsistent with observer-independence and, when corrected, is in agreement with the earlier argument that revealed the troublesome nonlocality. We further offer an alternative derivation for the energy-dependent speed of light in the model used.

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity, quantum mechanics, and observations

Abstract: Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.

Republication of: The mechanics of matter particles in general relativity

Abstract: This is an English translation of the first of two papers by Myron Mathisson, first published in German in 1931 and 1937, in which he presented the correct formulation of equations of motion of spinning bodies in general relativity (today known as the Mathisson–Papapetrou equations). The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note and Mathisson’s brief biography, both written by Andrzej Trautman.

Groupoid symmetry and constraints in general relativity. 1: kinematics

Abstract: When the vacuum Einstein equations are cast in the form of hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold M\Sigma\ of riemannian metrics on a Cauchy hypersurface \Sigma. As in every lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection.

On the consistency of the Horava Theory

Abstract: With the goal of giving evidence for the theoretical consistency of the Hořava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model. There have been a lot of interest about Hořava’s proposal of a new theory of gravity which in principle has a renormalizable quantum version [1] (an important part of the conceptual and technical basis was previously developed in Ref. [2]). To build such a theory, Hořava has proposed to abandon the principle of space-time relativity as a fundamental symmetry of nature, reducing the freedom to perform coordinate transformations to those transformations that preserve some preferred universal time-like foliation. The advantage of this scheme is that one can include higher spatial-derivative terms in the Lagrangian that render the theory renormalizable. According to Hořava’s point of view, jorgebellorin@usb.ve arestu@usb.ve

De Sitter Relativity and Cosmological Principle

Abstract: The formalism of Fantappie-Arcidiacono Projective General Relativity - also known as De Sitter Relativity - has recently been revised in order to make possible cosmological models with expansion, similarly to ordinary Fridman cosmology formulated within the context of General Relativity. In this article, several consequences of interest in the current cosmological debate are examined and discussed in a semiquantitative manner. Specifically: re-examination of the Supernova Project results using this new formalism, with a new estimate of the cosmological parameters; the ordinary matter to dark matter densities ratio; the existence of a new fundamental constant having the dimensions of an acceleration and its relation with dark matter.

Is exponential metric a natural space-time metric of Newtonian gravity ?

Abstract: We show how Newtonian gravity with effective (actually observed) masses, obeying the mass-energy relation of special relativity, can explain all observations used to test General relativity. Dynamics of a gravitationally coupled binary system is considered in detail, and the effective masses of constituents are determined. Interpreting our results in terms of motion in a curved space-time background, we are led, using the Lagrangian formalism, to consider the exponential metric as a natural space-time metric of Newtonian gravity.

On the relativity of rotation

Abstract: The question whether rotational motion is relative according to the general theory of relativity is discussed. Einstein’s ambivalence concerning this question is pointed out. In the present article I defend Einstein’s way of thinking on this when he presented the theory in 1916. The significance of the phenomenon of perfect inertial dragging in connection with the relativity of rotational motion is discussed. The necessity of introducing an extended model of the Minkowski spacetime, in which a globally empty space is supplied with a cosmic mass shell with radius equal to its own Schwarzschild radius, in order to extend the principle of relativity to accelerated and rotational motion, is made clear.