Showing papers on "Four-force published in 2000"
TL;DR: In this paper, a modification of the equation that must be satisfied by a Hamiltonian is proposed, which is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian.
Abstract: In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of the conserved quantity is defined to be the value of the Hamiltonian which generates the canonical transformation on phase space corresponding to this symmetry. However, such an approach cannot be employed to define ``conserved quantities'' in a situation where symplectic current can be radiated away (such as occurs at null infinity in general relativity) because there does not, in general, exist a Hamiltonian which generates the given asymptotic symmetry. (This fact is closely related to the fact that the desired ``conserved quantities'' are not, in general, conserved.) In this paper we give a prescription for defining ``conserved quantities'' by proposing a modification of the equation that must be satisfied by a Hamiltonian. Our prescription is a very general one, and is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian, although we have not investigated existence and uniqueness issues in the most general contexts. In the case of general relativity with the standard asymptotic conditions at null infinity, our prescription agrees with the one proposed by Dray and Streubel from entirely different considerations.
703 citations
129 citations
TL;DR: The iterated Crank-and-Nicholson method has become a popular algorithm in numerical relativity as mentioned in this paper, and it has been shown that one should carry out exactly two iterations and no more.
Abstract: The iterated Crank-Nicholson method has become a popular algorithm in numerical relativity. We show that one should carry out exactly two iterations and no more. While the limit of an infinite number of iterations is the standard Crank-Nicholson method, it can in fact be worse to do more than two iterations, and it never helps. We explain how this paradoxical result arises.
120 citations
95 citations
TL;DR: In this article, the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime were studied. But the authors focus on modes with zero speed of propagation and conjecture that they are responsible for instabilities encountered in numerical evolutions of the ADM.
Abstract: We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture that they are responsible for instabilities encountered in numerical evolutions of the ADM formulation. These zero speed modes are of two kinds: pure gauge modes and constraint violating modes. We show how the decoupling of the gauge by a conformal rescaling can eliminate the problem with the gauge modes. The zero speed constraint violating modes can be dealt with by using the momentum constraints to give them a finite speed of propagation. This analysis sheds some light on the question of why some recent reformulations of the 3+1 evolution equations have better stability properties than the standard ADM formulation.
86 citations
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TL;DR: In this paper, the fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described, including the field equations, the definition of an energy-momentum density for the gravitational field, the tele-parallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role playing by curvature in general relativity.
Abstract: The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described. In particular, the field equations, the definition of an energy--momentum density for the gravitational field, the teleparallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role played by curvature in general relativity, are discussed in some details.
76 citations
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01 Jan 2000
TL;DR: In this article, the authors present the historical background of Special Relativity Theory and the empirical confirmation of special Relativity theory, and the Elimination of absolute time and Relativistic Time.
Abstract: Preface. 1. The Historical Background of Special Relativity. 2. Einstein's Special Theory. 3. Time Dilation and Length Contraction. 4. Empirical Confirmation of Special Relativity. 5. Two Relativistic Interpretations. 6. The Classical Concept of Time. 7. The Positivistic Foundations of Relativity Theory. 8. The Elimination of Absolute Time. 9. Absolute Time and Relativistic Time. 10. God, Time, and Relativity. 11. Conclusion. Bibliography. Subject Index. Proper Name Index.
75 citations
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TL;DR: In this paper, a list of commented references of interest for embedded surfaces is provided, with a focus on the recent renewal in the interest for embedding surfaces, and a list is provided.
Abstract: Due to the recent renewal in the interest for embedded surfaces we provide a list of commented references of interest.
74 citations
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TL;DR: In this article, the representation of the mass point in general relativity has been studied and a short note by Marcel Brillouin on the representation has been given, which is paraphrases of the present paper.
Abstract: Short note by Marcel Brillouin on the representation of the mass point in general relativity.
55 citations
TL;DR: In this article, the cosmological constant is not a constant, in the same vein that energy in Einstein's Special Relativity is observer dependent, and the observed D = 4 world might just be an average dimension over the infinite possible values of the quantum space-time and why the compactification mechanisms from higher to four dimensions in string theory may not actually be the right way to look at the world at Planck scales.
Abstract: The stringy uncertainty relations, and corrections thereof, were explicitly derived recently from the new relativity principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck scale is the minimal length in nature in the same vein that the speed of light was taken as the maximum velocity in Einstein's theory of Special Relativity. A simple numerical argument is presented which suggests that quantum space-time may very well be infinite dimensional. A discussion of the repercussions of this new paradigm in Physics is given. A truly remarkably simple and plausible solution of the cosmological constant problem results from the new relativity principle: The cosmological constant is not a constant, in the same vein that energy in Einstein's Special Relativity is observer dependent. Finally, following El Naschie, we argue why the observed D =4 world might just be an average dimension over the infinite possible values of the quantum space-time and why the compactification mechanisms from higher to four dimensions in string theory may not be actually the right way to look at the world at Planck scales.
51 citations
TL;DR: In this article, several quantum mechanical wave equations for p-branes are proposed, which determine the quantum dynamics involving the creation/destruction of p-dimensional loops of topology Sp, moving in a D-dimensional spacetime background.
Abstract: This report is an extension of a previous one hep-th/9812189. Several quantum mechanical wave equations for p-branes are proposed. The most relevant p-brane quantum mechanical wave equations determine the quantum dynamics involving the creation/destruction of p-dimensional loops of topology Sp, moving in a D-dimensional spacetime background, in the quantum state Φ. To implement full covariance we are forced to enlarge the ordinary relativity principle to a new relativity principle, suggested earlier by the author based on the construction of C-space, and also by Pezzaglia's poly-dimensional relativity, where all dimensions and signatures of spacetime should be included on the same footing.
TL;DR: In this article, the definition of axial symmetry in general relativity is reviewed, and some results concerning the geometry in a neighbourhood of the axis are derived, and expressions for the metric are given in different coordinate systems, and emphasis is placed on how the metric coefficients tend to zero when approaching the axis.
Abstract: The definition of axial symmetry in general relativity is reviewed, and some results concerning the geometry in a neighbourhood of the axis are derived. Expressions for the metric are given in different coordinate systems, and emphasis is placed on how the metric coefficients tend to zero when approaching the axis. PACS numbers: 0420C, 0420J
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TL;DR: In this paper, a detailed comparison of the works of Lorentz and of Poincare up to 1904 is presented, showing that both authors succeeded in constructing a coherent and fully relativistic theory, although their ideas about the ether were radically different.
Abstract: Special relativity was discovered at the eve of the century, but finds its roots in the 19th century efforts to understand the optics and electromagnetism of moving bodies. These roots are reviewed in Parts 1 and 2, the latter being specially devoted to the works of Lorentz and of Poincare up to 1904. Part 3 contains a detailed comparison of the works of Einstein and of Poincare in 1905. It is shown that both authors succeeded in constructing a coherent and fully relativistic theory, although their ideas about the ether were radically different. In Part 4, the question of the respective merits of the three potential fathers of special relativity (i.e. Lorentz, Poincare, Einstein) is discussed again, at the light of the preceding analysis and of the "post-1905" developments of the theory.
TL;DR: In this article, the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor are discussed and algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form are presented.
Abstract: This is the first in a series of papers concerning a project to set up a computer database of exact solutions in general relativity which can be accessed and updated by the user community. In this paper, we briefly discuss the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor. We then present algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form.
TL;DR: The notion of geometrical duality is discussed in this paper in the context of both Brans-Dicke theory and general relativity, and it is shown that the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity).
Abstract: The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity). This dual representation provides a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.
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01 Jan 2000Posted Content•
TL;DR: In this article, different approaches to special relativity (SR) are discussed, including invariant, covariant and non-covariant approaches, where some quantities are not tensor quantities, but rather quantities from 3+1 space and time, eg, the synchronously determined spatial length.
Abstract: Different approaches to special relativity (SR) are discussed The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based geometric quantities comprising both components and a basis This approach we call the ''true transformations (TT) relativity'' It is compared with the usual covariant approach, which mainly deals with the basis components of true tensors The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from ''3+1'' space and time, eg, the synchronously determined spatial length This formulation is called the ''apparent transformations (AT)\ relativity'' The spacetime length is considered in the ''TT relativity'' and spatial and temporal distances in the ''AT relativity'' It is also found that the usual transformations of the three-vectors of the electric and magnetic fields $\QTR{bf}{E}$ and $\QTR{bf}{B}$ are the AT The Maxwell equations with $F^{ab}$ are written in terms of the 4-vectors of the electric $E^{a}$ and magnetic $B^{a}$ fields The covariant Majorana electromagnetic field 4-vector $\Psi ^{a}$ is constructed by means of 4-vectors $E^{a}$ and $B^{a}$ and the covariant Majorana formulation of electrodynamics is presented A Dirac like relativistic wave equation for the free photon is obtained
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10 Feb 2000
TL;DR: In this article, the authors present an integrated treatment of classical mechanics and special relativity by treating classical mechanics as Galilean relativity, which gives students the freedom to formulate a particular problem in one frame of reference and solve it in another, where it takes a simpler form.
Abstract: Special relativity suffers from the myth that it is difficult In order to overcome this barrier Dynamics and relativity presents an integrated treatment of classical mechanics and special relativity, by treating classical mechanics as Galilean relativity This gives students the freedom to formulate a particular problem in one frame of reference and solve it in another, where it takes a simpler form This strategy, which is central to special relativity, is applied to problems in classical mechanics, thus preparing the tools and thought patterns for a treatment of special relativity
TL;DR: In this article, the spin-gravity-electromagnetism coupling is investigated for motion in the background of a Reissner-Nordstrom black hole both in the exact spacetime and in the weak-field approximation.
Abstract: The dynamics of a charged spinning test particle in general relativity is studied in the context of gravitoelectromagnetism. Various families of test observers and supplementary conditions are examined. The spin-gravity-electromagnetism coupling is investigated for motion in the background of a Reissner-Nordstr\"om black hole both in the exact spacetime and in the weak-field approximation. Results are compared with those of the theory.
TL;DR: In this paper, the theory of measurement is employed to elucidate the physical basis of general relativity and a nonlocal theory of accelerated observers is briefly described that is consistent with observation and excludes the possibility of existence of a fundamental scalar field in nature.
Abstract: The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational and rotational) scales characteristic of the motion of the observer. Thus general relativity is a consistent theory of coincidences so long as these involve classical point particles and electromagnetic rays (geometric optics). Wave optics is discussed and the limitations of the standard theory in this regime are pointed out. A nonlocal theory of accelerated observers is briefly described that is consistent with observation and excludes the possibility of existence of a fundamental scalar field in nature.
12 May 2000
TL;DR: In this article, a class of vacuum initial-data sets is described which are based on certain expressions for the extrinsic curvature first studied and employed by Bowen and York, which play a role for the momentum constraint of General Relativity which is analogous to the role played by the Coulomb solution for the Gau\-law constraint of electromagnetism.
Abstract: A class of vacuum initial-data sets is described which are based on certain expressions for the extrinsic curvature first studied and employed by Bowen and York These expressions play a role for the momentum constraint of General Relativity which is analogous to the role played by the Coulomb solution for the Gau\-law constraint of electromagnetism
TL;DR: A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found in this article, where the same authors also present a solution to a similar problem in the case of a thin shell.
Abstract: A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.
TL;DR: In this article, it was shown that residual errors in the Regge calculus cannot be used to distinguish metrics which are solutions of Einstein's equations from those that are not, and that it is incorrect to use residual errors as a criteria to judge the discrete equations.
Abstract: We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors cannot be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.
01 Jan 2000
TL;DR: In this paper, the authors suggest that there are fairly prosaic physical circumstances under which it might not be entirely beside the point to look around for observable violations of the special theory of relativity.
Abstract: There seems to me to be a way of reading some of the trouble we have lately been having with the quantum-mechanical measurement problem (not the standard way, mind you, and certainly not the only way; but a way that nonethe-less be worth exploring) that suggests that there are fairly prosaic physical circumstances under which it might not be entirely beside the point to look around for observable violations of the special theory of relativity. The suggestion I have in mind is connected with attempts over the past several years to write down a relativistic field-theoretic version of the dynamical reduction theory of Ghirardi, Rimini, and Weber [Physical Review D34, 470-491 (1986)], or rather it is connected with the persistent failure of those attempts, it is connected with the most obvious strategy for giving those attempts up. And that (in the end) is what this paper is going to be about.
TL;DR: In this article, the authors discuss the relation between Relativity before 1905 and special Relativity-Kinematics and its kinetics, including Arbitrary Frames, Surfaces and Curvature, and Intrinsic Geometry.
Abstract: 1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.
TL;DR: In this article, it was shown that models of elementary particles in classical general relativity (geons) will naturally have the transformation properties of a spinor if the spacetime manifold is not time orientable.
Abstract: It is shown that models of elementary particles in classical general relativity (geons) will naturally have the transformation properties of a spinor if the spacetime manifold is not time orientable. From a purely pragmatic interpretation of quantum theory this explains why spinor fields are needed to represent particles. The models are based entirely on classical general relativity and are motivated by the suggestion that the lack of a time-orientation could be the origin of quantum phenomena.
TL;DR: In this article, a special Relativity with Acceleration (SRAD) model is proposed. But the model is not suitable for the special case of special geometry with acceleration (SRI).
Abstract: (2000). Special Relativity with Acceleration. The American Mathematical Monthly: Vol. 107, No. 3, pp. 219-237.
TL;DR: This work considers general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory, the lambda --> infinity limit of general relativity, which allows an explicit perturbation computational setup in which the quantum states of the theory and the classical observables can be explicitly computed.
Abstract: We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.
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TL;DR: In this paper, the authors make the second claim precise in the form of a modest no-go theorem, which they use to show that none of the criteria fully answers to our classical intuitions.
Abstract: Within the framework of general relativity, in some cases at least, it is a delicate and interesting question just what it means to say that an extended body is or is not "rotating". It is so for two reasons. First, one can easily think of different criteria of rotation. Though they agree if the background spacetime structure is sufficiently simple, they do not do so in general. Second, none of the criteria fully answers to our classical intuitions. Each one exhibits some feature or other that violates those intuitions in a significant and interesting way. The principal goal of the paper is to make the second claim precise in the form of a modest no-go theorem.