Showing papers on "Four-force published in 2009"

The Formation of Black Holes in General Relativity

Abstract: The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first foray into the long time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitably small neighborhood of Minkowskian data. The theorems are general, no symmetry conditions on the initial data being imposed.

The Cauchy Problem in General Relativity

Abstract: After a brief introduction to classical relativity, we describe how to solve the Cauchy problem in general relativity. In particular, we introduce the notion of gauge source functions and explain how they can be used in order to reduce the problem to that of solving a system of hyperbolic partial differential equations. We then go on to explain how the initial value problem is formulated for the so-called Einstein-Vlasov system, and describe a recent future global non-linear stability result in this setting. In particular, this result applies to models of the universe which are consistent with observations.

Recovering General Relativity from Massive Gravity

Abstract: We obtain static, spherically symmetric, and asymptotically flat numerical solutions of massive gravity with a source. Those solutions show, for the first time explicitly, a recovery of the Schwarzschild solution of general relativity via the so-called Vainshtein mechanism.

General very special relativity in Finsler cosmology

Abstract: General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.

Drawing the line between kinematics and dynamics in special relativity

Abstract: In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz’s classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz’s theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in the early reception of special relativity in the physics literature: the Fresnel drag eect in the Fizeau experiment, the velocity dependence of electron mass in -ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I oer historical sketches of how Lorentz’s dynamical explanations of

A type of born-infeld regular gravity and its cosmological consequences

Abstract: Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld parameter λ bounds the dynamics of Hubble parameter H(t) and establishes a maximum attainable spacetime curvature.

The extended relativity theory in clifford spaces

Abstract: An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose "point" coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes.... degrees of freedom associated with the collective particle, string, membrane, p-brane,... dynamics of p-loops (closed p-branes) in target Ddimensional spacetime backgrounds. C-space Relativity naturally incorporates the ideas of an invariant length (Planck scale), maximal acceleration, non-commuting coordinates, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (closed) p-branes, for all values of p, on a unified footing. It resolves the ordering ambiguities in QFT, the problem of time in Cosmology and admits superluminal propagation ( tachyons ) without violations of causality. A discussion of the maximalacceleration Relativity principle in phase-spaces follows and the study of the invariance group of symmetry transformations in phase-space allows to show why Planck areas are invariant under acceleration-boosts transformations . This invariance feature suggests that a maximal-string tension principle may be operating in Nature. We continue by pointing out how the relativity of signatures of the underlying n-dimensional spacetime results from taking different n-dimensional slices through C-space. The conformal group in spacetime emerges as a natural subgroup of the Clifford group and Relativity in C-spaces involves natural scale changes in the sizes of physical objects without the introduction of forces nor Weyl's gauge field of dilations. We finalize by constructing the generalization of Maxwell theory of Electrodynamics of point charges to a theory in C-spaces that involves extended charges coupled to antisymmetric tensor fields of arbitrary rank. In the concluding remarks we outline briefly the current promising research programs and their plausible connections with C-space Relativity.

The Confrontation Between General Relativity and Experiment

Abstract: We review the experimental evidence for Einstein’s general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.

Rotation in relativity and the propagation of light

Abstract: We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a coordinate system or induced by the curvature of spacetime, and (ii) computer visualizations which bring out the alien features of the Goedel Universe. In order to keep the paper self-contained, we summarize in several appendices crucial ingredients of the mathematical tools used in general relativity. In this way, our lecture notes should be accessible to researchers familiar with the basic elements of tensor calculus and general relativity.

The Box-Problem in Deformed Special Relativity

Abstract: We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what constitutes the same space-time event becomes dependent on the observer's inertial frame. To preserve observer-independence, the such arising nonlocality should not be in conflict with our knowledge of particle interactions. This requirement allows us to derive strong bounds on deformations of Special Relativity and rule out a modification to first order in energy over the Planck mass.

Diffusion in the special theory of relativity

Abstract: The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Juttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

A spherically symmetric and stationary universe from a weak modification of general relativity

Abstract: It is shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the universe. This is due to the presence of a third mode of polarization in the linearized gravity in which a "curvature" energy term is present. Such an energy can, in principle, be identified as the Dark Energy. The model can also help to a better understanding of the framework of the Einstein-Vlasov system.

Optics of rotating systems

Abstract: Electrodynamics of rotating systems is expected to exhibit novel nonlocal features that come about when acceleration-induced nonlocality is introduced into the special relativity theory in conformity with the Bohr-Rosenfeld principle. The implications of nonlocality for the amplitude and frequency of electromagnetic radiation received by uniformly rotating observers are investigated.

Einstein's Special Relativity: The Hyperbolic Geometric Viewpoint

Abstract: The analytic hyperbolic geometric viewpoint of Einstein's special theory of relativity is presented. Owing to the introductio n of vectors into hyperbolic geometry, where they are called gyrovectors, the use of analytic hyperbolic geometry extends Einstein's unfinished symphony significantly, elev ating it to the status of a mathematical theory that could be emulated to the benefit of t he entire mathematical and physical community. The resulting theory involves a gyrovector space approach to hyperbolic geometry and relativistic mechanics, and could be studied with profit by anyone with a sufficient background in the common vector spac e approach to Euclidean geometry and classical mechanics. Einstein noted in his 1905 paper that founded the special theory of relativity that his velocity addition law satisfies the law of velocity parallelogram only to a first approximation. Within our hype rbolic geometric viewpoint of special relativity it becomes clear that Einstein's velo city addition law leads to a hyperbolic parallelogram addition law of Einsteinian velocities, which is supported experimentally by the cosmological effect known as stellar aberration and its relativistic interpretation. The latter, in turn, is supported experime ntally by the "GP-B" gyroscope experiment developed by NASA and Stanford University. Furthermore, the hyperbolic viewpoint of special relativity meshes extraordinarily well with the Minkowskian four- vector formalism of special relativity, revealing that the seemingly notorious relativistic mass meshes up with the four-vector formalism as well, owing to the natural emergence of dark matter. It is therefore hoped that both special relativity and its u nderlying analytic hyperbolic geometry will become part of the lore learned by all undergraduate and graduate mathematics and physics students.

The gravitational origin of the distinction between space and time

Abstract: To the ordinary human it is obvious that there is a clear distinction between the spatial dimensions, in which one can go either way, and the temporal dimension, in which one seems only to move forward. But the uniqueness of time is also rooted in the standard presentation of general relativity, in which the metric of space–time is locally Lorentzian, i.e. ημν = diag(1, -1, -1, -1). This is presented as an independent axiom of the theory, which cannot be deduced. In this essay I will claim otherwise. I will show that the existence of time should not be enforced on the gravitational theory of general relativity but rather should be deduced from it. The method of choice is linear stability analysis of flat space–times.

Two approaches to testing general relativity in the strong-field regime

Abstract: Observations of compact objects in the electromagnetic spectrum and the detection of gravitational waves from them can lead to quantitative tests of the theory of general relativity in the strong-field regime following two very different approaches. In the first approach, the general relativistic field equations are modified at a fundamental level and the magnitudes of the potential deviations are constrained by comparison with observations. In the second approach, the exterior spacetimes of compact objects are parametrized in a phenomenological way, the various parameters are measured observationally, and the results are finally compared against the general relativistic predictions. In this article, I discuss the current status of both approaches, focusing on the lessons learned from a large number of recent investigations.

Even the Minkowski space is holed

Abstract: To cure the lack of predictive power of general relativity, Geroch proposed to complete the theory with an additional postulate that only 'hole-free' spacetimes are permitted. This postulate (or, rather, that obtained from it by some disambiguating) seems physically well-founded and at the same time appropriately restrictive. I show, however, that it is too strong--it prohibits even the Minkowski space.

Quasilocal Energy in General Relativity

Abstract: We show that the quasilocal mass defined by Wang and Yau is not well-defined at spatial infinity. It approaches neither the ADM mass nor the ADM energy. We suggest an alternative scheme which retains all the desirable characteristics of the Wang-Yau mass and, in addition, asymptotes to the ADM energy at infinity.

Introduction to Gravitational Self-Force

Abstract: The motion of a sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be “gravitational self-force” corrections to geodesic motion, analogous to the “radiation reaction forces” that occur in electrodynamics. It is of considerable importance to be able to calculate these self-force corrections in order to be able to determine such effects as inspiral motion in the extreme mass ratio limit. However, severe difficulties arise if one attempts to consider point particles in the context of general relativity. This article describes these difficulties and how they have been dealt with.

Bianchi Type-III stiff fluid cosmological model in general relativity

Abstract: In this paper, we have investigated a tilted Bianchi Type-III stiff fluid cosmological model in general relativity. To get a determinate solution, we have assumed a condition A=(BC)n between metric potentials. The various physical and geometrical aspects of the model are discussed.

Experimental Basis for Special Relativity in the Photon Sector

Abstract: A search of the literature reveals that none of the five new optical effects predicted by the special theory of relativity have ever been observed to occur in nature. In particular, the speed of light (c) has never been measured directly with a moving detector to validate the invariance of c to motion of the observer, a necessary condition for the Lorentz invariance of c. The invariance of c can now only be inferred from indirect experimental evidence. It is also not widely recognized that essentially all of the experimental support for special relativity in the photon sector consists of null results. The experimental basis for special relativity in the photon sector is summarized, and concerns about the completeness, integrity and interpretation of the present body of experimental evidence are discussed.

Explicit gauge covariant Euler–Lagrange equation

Abstract: The application of a gauge covariant derivative to the Euler–Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic part of the derivative and hence simplifies Lagrangians containing tensor and gauge covariant fields. The gauge covariant derivative used in the covariant Euler–Lagrange equation is presented as an extension of the coordinate covariant derivative used in tensor analysis. Several examples provide useful demonstrations of the covariant derivative relevant to studies in general relativity and gauge theory.

Time and Causation

Abstract: In this review paper, we consider the fundamental nature of time and causality, most particularly, in the context of the theories of special and general relativity. We also discuss the issue of closed timelike curves in the context of general relativity, and the associated paradoxes, the question of directionality of the time flow and, rather briefly, the problem of time in quantum gravity.

The principle of relativity and inertial dragging

Abstract: Mach’s principle and the principle of relativity have been discussed by Hartman and Nissim-Sabat. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested by Bhadra and Das. However, neither set of authors allowed for the general relativistic phenomenon of inertial dragging, and no calculation was offered to substantiate their claims. I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativity and discuss the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculations to demonstrate how these points arise as consequences of the general theory of relativity.

Outer Boundary Conditions in Numerical Relativity

Abstract: This thesis is concerned with outer boundary conditions in numerical relativity. In numerical simulations, the spatially infinite universe is typically modelled using a finite spatial domain, on the edge of which boundary conditions are imposed. These boundary conditions should mirror the unbounded physical domain as closely as possible. They should be transparent to outgoing gravitational radiation and should not introduce spurious incoming radiation via reflections of outgoing radiation off the boundary. The concepts of incoming and outgoing gravitational radiation are only well understood in certain specific charts and tetrads. The first half of this thesis investigates the relationship between these charts and tetrads and those used in numerical relativity. We begin by studying a previous calculation [134], in which quantities such as the Bondi mass and the news function were expressed in terms of the Newman-Penrose scalars in an axisymmetric spacetime. The calculation is generalized to spacetimes with no symmetries. The results above still require a specific choice of tetrad. By supposing that the region of spacetime far from an isolated gravitating source is in some sense Minkowskian, we demonstrate how to transform between the charts and tetrads used in theoretical studies of gravitational radiation and the charts and tetrads used in numerical relativity. This enables us to provide “numerical relativity recipes” in which the Weyl scalars, the Bondi mass and news function are expressed in terms of the metric variables in a numerical chart. The second half of this thesis addresses the problem of absorbing boundary conditions in numerical relativity. Using Hertz potentials, the far-field region of a spacetime can be expressed as a linear perturbation about Minkowski, Schwarzschild or Kerr backgrounds. The resulting field equations enable us to investigate the propagation of linearized gravitational radiation. On a Minkowski background, incoming and outgoing waves propagate independently. The presence of a curved background creates a “gravitational tail” whose behaviour near future null infinity we are able to estimate. This enables us to formulate absorbing boundary conditions for numerical relativity. Finally, we link the two threads mentioned above. The boundary conditions are expressed in terms of the metric variables in a numerical relativity chart.