Showing papers on "Four-force published in 1999"

Self-similarity in general relativity

Abstract: The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the `first' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally, we consider more general types of self-similar models.

Spherically Symmetrical Models in General Relativity

Abstract: The field equations of general relativity areapplied to pressure-free spherically symmetrical systemsof particles The equations of motion are determinedwithout the use of approximations and are compared with the Newtonian equations The total energyis found to be an important parameter, determining thegeometry of 3-space and the ratio of effectivegravitating to invariant mass The Doppler shift isdiscussed and is found to contain both the velocity shiftand the Einstein shift combined in a rather complexexpression

The expanding worlds of general relativity

Abstract: I Relativity in the Making- The Search for Gravitational Absorption in the Early Twentieth Century- Minkowski, Mathematicians, and the Mathematical Theory of Relativity- Heuristics and Mathematical Representation in Einstein's Search for a Gravitational Field Equation- Rotation as the Nemesis of Einstein's Entwurf Theory- II Relativity at Work- Einstein, Relativity and Gravitation Research in Vienna before 1938- Controversies in the History of the Radiation Reaction Problem in General Relativity- The Penrose-Hawking Singularity Theorems: History and Implications- III Relativity at Large- The Cosmological Woes of Newtonian Gravitation Theory- Genesis and Evolution of Weyl's Reflections on De Sitter's Universe- Milne, Bondi and the 'Second Way' to Cosmology- Steady-State Cosmology and General Relativity: Reconciliation or Conflict?- IV Relativity in Debate- Larmor versus General Relativity- Kretschmann's Analysis of Covariance and Relativity Principles- Point Coincidences and Pointer Coincidences: Einstein on the Invariant Content of Space-Time Theories- Contributors

The origin of the spacetime metric: Bell's ‘Lorentzian pedagogy’ and its significance in general relativity

Abstract: The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general relativity.

Minkowski, Mathematicians, and the Mathematical Theory of Relativity

Abstract: T HE IMPORTANCE OF THE THEORY OF RELATIVITY for twentieth-century physics, and the appearance of the Gottingen mathematician Hermann Minkowski at a turning point in its history have both attracted significant historical attention. The rapid growth in scientific and philosophical interest in the principle of relativity has been linked to the intervention of Minkowski by Tetu Hirosige, who identified Minkowski’s publications as the turning point for the theory of relativity, and gave him credit for having clarified its fundamental importance for all of physics (Hirosige 1968: 46; 1976: 78). Lewis Pyenson has placed Minkowski’s work in the context of a mathematical approach to physics popular in Gottingen, and attributed its success to the prevalence of belief in a neo-Leibnizian notion of pre-established harmony between pure mathematics and physics (Pyenson 1985, 1987: 95). The novelty to physics of the aesthetic canon embodied in Minkowski’s theory was emphasized by Peter Galison (1979), and several scholars have clarified technical and epistemological aspects of Minkowski’s theory. In particular, the introduction of sophisticated mathematical techniques to theoretical physics by Minkowski and others is a theme illustrated by Christa Jungnickel and Russell McCormmach. In what follows, we address another aspect of Minkowski’s role in the history of the theory of relativity: his disciplinary advocacy. Minkowski’s 1908 Cologne lecture “Raum und Zeit” (Minkowski 1909) may be understood as an effort to ex-

General Relativity: A Geometric Approach

Abstract: Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear and concise introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.

A Century of Relativity

Abstract: Except for quantum mechanics—a more than modest exception—relativity has been the most profound conceptual advance in 20th century physics. Both in developing special and general relativity, Albert Einstein’s hallmark was to anchor his theory on a few simple but profound principles. The results have provided endless fascination and puzzlement to the general public, and have had an enormous impact on our conceptual framework for understanding nature.

Classical and Quantum Gravity on Conformal Superspace

Abstract: The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of a four-dimensional gauge group of arbitrary coordinate and conformal transformations of riemannian metrics defined on a three-manifold This new symmetry is more restrictive and hence more predictive Many of the difficulties that have plagued the canonical quantization of general relativity seem to vanish

Speed limits in general relativity

Abstract: Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994 The warp drive: hyper-fast travel within general relativity Class. Quantum Grav. 11 L73-7) in the absence of exotic matter.

On the Foundation of the Principle of Relativity

Abstract: The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call “Aristotle's first and second laws.” An “Aristotelian” universe in which all motion is relative to “absolute space” is considered. The first law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in “true” gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed.

Introduction to the Relativity Principle

Abstract: Preliminaries. The Relativity Principle, and its Applications in Newtonian Physics. Einstein's Relativity Principle. KINEMATICS. Lorentz Transformations. Invariant Intervals and Space-Time Diagrams. Proper Time and Nonuniform Motion. Four-Vectors. Four-Acceleration. MOMENTUM AND ENERGY. Particle Dynamics: Momentum and Energy. Natural Units, and the Prevalence of MeV. Systems of Particles: Four-Momentum Conservation using Invariants. WAVES. Plane Waves. Light Waves in Empty Space: Aberration and Doppler Effect. Appendices. Problems. Index.

New numerical scheme to compute three-dimensional configurations of quasiequilibrium compact stars in general relativity: Application to synchronously rotating binary star systems

Abstract: We develop a new numerical scheme to obtain quasiequilibrium structures of binary neutron star systems and nonaxisymmetric compact stars as well as the space time around those systems in general relativity. Although, strictly speaking, there are no equilibrium states for binary configurations in general relativity, the time scale of changes in orbital motion due to gravitational wave radiation is long compared with the orbital period. Thus, we can assume that binary neutron star systems, and nonaxisymmetric systems in general are in ``quasiequilibrium'' states. Concerning the quasiequilibrium states of binary systems in general relativity, several investigations have been already carried out by assuming conformal flatness of the spatial part of the metric. However, the validity of the conformally flat treatment has not been fully analyzed except for axisymmetric configurations. Therefore, it is desirable to solve for the quasiequilibrium states by developing totally different methods from the conformally flat scheme. In this paper, we present a new numerical scheme to solve the Einstein equations for three-dimensional configurations directly, without assuming conformal flatness, although we use the simplified metric for the space time. This new formulation is an extension of the scheme which has been successfully applied for structures of axisymmetric rotating compact stars in general relativity. It is based on the integral representation of the Einstein equations, and takes into account the boundary conditions at infinity. We have checked our numerical scheme by computing equilibrium sequences of binary polytropic star systems in Newtonian gravity and those of axisymmetric polytropic stars in general relativity. We have applied this numerical code to binary star systems in general relativity and have succeeded in obtaining several equilibrium sequences of synchronously rotating binary polytropes with the polytropic indices $N=0.0,$ $0.5,$ and $1.0.$ It should be noted that our equilibrium sequences are not those of constant baryon mass star models because there is no unique choice of parameters to keep the baryon mass constant for our polytropic relation.

Existence and uniqueness of solutions to characteristic evolution in Bondi-Sachs coordinates in general relativity

Abstract: We show that the theorem of Duff on the existence and uniqueness of solutions to linear characteristic initial-value problems holds in the case of linearized characteristic evolution in Bondi-Sachs coordinates in general relativity. This represents the characteristic equivalent to the manifest existence and uniqueness of the case of standard Cauchy problems. This extends Sachs' original work on the characteristic approach to the Einstein equations, by considering a null-timelike approach rather than a null-asymptotic one.

A New Look at Relativity Transformations

Abstract: A free system, considered to be a comparisonsystem, allows for the notion of objective existence andinertial frame. Transformations connecting inertialframes are shown to be either Lorentz or generalizedGalilei.

An Introduction to Relativistic Gravitation

Abstract: This is an introductory textbook on applications of general relativity to astrophysics and cosmology. The aim is to provide graduate students with a toolkit for understanding astronomical phenomena that involve velocities close to that of light or intense gravitational fields. The approach taken is first to give the reader a thorough grounding in special relativity, with space-time the central concept, following which general relativity presents few conceptual difficulties. Examples of relativistic gravitation in action are drawn from the astrophysical domain. The book can be read on two levels: first as an introductory fast-track course, and then as a detailed course reinforced by problems which illuminate technical examples. The book has extensive links to the literature of relativistic astrophysics and cosmology.

God's Equation: Einstein, Relativity, and the Expanding Universe

Abstract: Drawing on newly discovered letters of Einstein--many translated here for the first time--years of research, and interviews with prominent mathematicians, cosmologists, physicists, and astronomers, Aczel takes us on a fascinating journey into "the strange geometry of space-time," and into the mind of a genius. Here the unthinkable becomes real: an infinite, ever-expanding, ever-accelerating universe whose only absolute is the speed of light.

Complex Geometry of Nature and General Relativity

Abstract: An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.

Degeneracy of the b-boundary in General Relativity

Abstract: The b-boundary construction by B. Schmidt is a general way of providing a boundary to a manifold with connection [12]. It has been shown to have undesirable topological properties however. C. J. S. Clarke gave a result showing that for space-times, non-Hausdorffness is to be expected in general [3], but the argument contains some errors. We show that under somewhat different conditions on the curvature, the b-boundary will be non-Hausdorff, and illustrate the degeneracy by applying the conditions to some well known exact solutions of general relativity.

Generating rotating fields in general relativity

Abstract: I present a new method to generate rotating solutions of the Einstein-Maxwell equations from static solutions, give several examples of its application, and discuss its general properties.

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

Abstract: Albert Einstein’s 1907 Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.

Discrete and finite general relativity

Abstract: We develop the general theory of relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The essence of this approach is of working with fields defined with support on straight lines and not on hypersurfaces as usual. The general relativity homogeneous field equations are then solved for a finite, singularity-free, point-like field that we associate with a `classical graviton'. The standard Einstein continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chosen imposed symmetry. The Schwarzschild metric is obtained by imposing spherical symmetry on the averaged field.

Gauss vs Coulomb and the Cosmological Mass-deficit Problem

Abstract: In a previous work General Relativity has been presented as a microscopic theory of finite and discrete point-like fields that we associate to a classical description of gravitons. The standard macroscopic continuous field is retrieved as an average-valued field through an integration over these gravitons. Here we discuss extreme alternative (the Gauss's and the Coulomb's) ways of obtaining and interpreting the averaged fields, how they depend on the kind of measurements involved, and how do they fit with the experimental data. The field measurements in the classical tests of general relativity correspond to the Coulomb's mode whereas the determination of the overall spacetime curvature in a cosmological scale is clearly a Gauss's mode. As a natural consequence there is no missing mass and, therefore, no such a need of dark mass as the value predicted by General Relativity, in the context of the Gauss's mode, agrees with the observed one.