scholarly journals VACUUMLESS COSMIC STRINGS IN BRANS–DICKE THEORY

2001 ◽  
Vol 10 (04) ◽  
pp. 515-522 ◽  
Author(s):  
A. A. SEN
Keyword(s):  
General Relativity ◽  
Cosmic Strings ◽  
Gravitational Effect ◽  
Weak Field ◽  
Field Equations ◽  
Gravitational Fields

The gravitational fields of vacuumless global and gauge strings have been studied in Brans–Dicke theory under the weak field assumption of the field equations. It has been shown that both global and gauge string can have repulsive as well as attractive gravitational effect in Brans–Dicke theory which is not so in General Relativity.

Relativity Made Relatively Easy Volume 2

2021 ◽  
Author(s):  
Andrew M. Steane
Keyword(s):  
General Relativity ◽  
Classical Field Theory ◽  
Weak Field ◽  
Stellar Structure ◽  
Field Equations ◽  
Graduate Course ◽  
Entry Level ◽  
Introductory Course ◽  
Penrose Process ◽  
Low Amplitude

This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.

scholarly journals "Gravitationally Lensed Gravitation" (GLG)

2021 ◽  
Author(s):  
Andreas Boenke
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Free Fall ◽  
Gravitational Effect ◽  
Gravitational Lens ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Optical Illusions ◽  
Spacetime Curvature ◽  
Background Object

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

scholarly journals On electric phenomena in gravitational fields

1927 ◽  
Vol 116 (775) ◽  
pp. 720-735 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Wave Length ◽  
Gravitational Effect ◽  
Electromagnetic Theory ◽  
Relativity Theory ◽  
Elementary Functions ◽  
Field Equations ◽  
Gravitational Fields ◽  
Particular Solutions

It is a consequence of general relativity that all electromagnetic and optical phenomena are influenced by a gravitational field. Indeed, the first prediction of relativity-theory, namely, the bending of light-rays when they pass near a massive body such as the sun, was a p articular application of this principle. Evidently, therefore, the classical electromagnetic theory must be rewritten in order to take account of the interaction between electromagnetism and gravitation; but beyond laying down general principles, comparatively little progress has been made hitherto in this task, the mathematical difficulties of solving definite electrical problems in a gravitational field being somewhat formidable. The subject is, however, of some interest to atomic physics; for if we assume that the atom has a massive nucleus with electrons in its immediate neighbourhood, the behaviour of such electrons (especially with regard to radiation) will be affected by the gravitational field of the nucleus. In the present paper two kinds of gravitational field are considered, namely, the field due to a single attracting centre ( i, e ., the field whose metric was discovered by Schwarzschild) and a limiting form of it. Within these gravita­tional fields we suppose electromagnetic fields to exist. Strictly speaking, the electromagnetic field has itself a gravitational effect, i.e. , it changes the metric everywhere; but this effect is in general; small, and we shall treat the ideal case in which it is ignored, so we shall suppose the metric to be simply that of the gravitational field originally postulated. The general equations of the electro­magnetic field are obtained, and particular solutions are found, which are the analogues of well-known particular solutions in the classical electromagnetic theory; notably the fields due to electrons at rest, electrostatic fields in general, and spherical electromagnetic waves. The results of the investigation are for the most part expressible only in terms of Bessel functions and certain new functions which are introduced; but in some interesting cases the electro­magnetic phenomena can be represented in term s of elementary functions, as, for instance, the electric field due to an electron in a quasi-uniform gravitational field (equations (15) and (19) below) and the spherical electromagnetic waves of short wave-length about a gravitating centre (equation (43) below).

Global General Relativity

1979 ◽  
Vol 368 (1732) ◽  
pp. 19-21
Keyword(s):  
General Relativity ◽  
High Speed ◽  
Equations Of State ◽  
Perturbation Expansion ◽  
Theoretical Work ◽  
Field Equations ◽  
Gravitational Fields ◽  
Highly Nonlinear ◽  
Mathematical Techniques ◽  
Algebraic Forms

Much of the theoretical work that has been carried out in General Relativity, particularly in the earlier years of the subject, has been concerned with finding explicit solutions of Einstein’s field equations, either in the vacuum case or, with suitable equations of state, when matter is present. These have been very useful in giving us some sort of feeling for the nature of more general ‘ physically reasonable ’ solutions, but they can, at best, only be rough approximations to such solutions. Exact solutions must, owing to the limitations of human energy and ingenuity, and to the complexity of Einstein’s equations, involve a number of simplifying assumptions, such as special symmetries or particular algebraic forms for the metric or curvature. Sometimes it is legitimate to regard such a special solution as the first term in some perturbation expansion towards something more realistic. But in the highly nonlinear situations of strong gravitational fields, such as in gravitational collapse to a black hole, or perhaps also in cosmology, it is often not clear when the results of such perturbation calculations (themselves often very complicated) can be trusted. High-speed computers can come to our aid (Smarr 1979, this symposium), of course, and can often give important insights in particular situations. But complementary to these are the global qualitative mathematical techniques that have been introduced into relativity over the past several years (Hawking & Ellis 1973; Penrose 1972).

scholarly journals Four interactions in the sedenion curved spaces

2019 ◽  
Vol 16 (02) ◽  
pp. 1950019 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Flat Space ◽  
Field Equations ◽  
Curved Space ◽  
Gravitational Fields ◽  
Curved Spaces ◽  
Spatial Parameters ◽  
Physical Quantities

The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. Maxwell was the first to utilize the quaternions to describe the property of electromagnetic fields. Nowadays, the scholars introduce the complex-octonions to depict the electromagnetic and gravitational fields. And the complex-sedenions can be applied to study the field equations of the four interactions in the classical mechanics and quantum mechanics. Further, it is able to extend the field equations from the flat space into the curved space described with the complex-sedenions, by means of the tangent-frames and tensors. The research states that a few physical quantities will make a contribution to certain spatial parameters of the curved spaces. These spatial parameters may exert an influence on some operators (such as, divergence, gradient, and curl), impacting the field equations in the curved spaces, especially, the field equations of the four quantum-fields in the quantum mechanics. Apparently, the paper and General Relativity both confirm and succeed to the Cartesian academic thought of ‘the space is the extension of substance’.

scholarly journals Generalized transformations and coordinates for static spherically symmetric general relativity

2018 ◽  
Vol 5 (4) ◽  
pp. 171109
Author(s):  
James M. Hill ◽  
Joseph O'Leary
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Weak Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Weak Field Limit ◽  
Spherically Symmetric Solution ◽  
Coordinate Singularity ◽  
Orthogonal Line

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates.

On the Born approximation for perturbations of a spherical star and the Newman—Penrose constants

1973 ◽  
Vol 335 (1601) ◽  
pp. 163-190 ◽  
Keyword(s):  
General Relativity ◽  
Born Approximation ◽  
Weak Field ◽  
Far Field ◽  
Field Equations ◽  
Stationary Source

The field equations governing perturbations of a spherical star in general relativity are solved by means of a weak field or Born approximation. Formal expressions for the far field of a non-stationary source are obtained and used to discuss the Newman-Penrose constants.

scholarly journals An Approach to Colliding Plane Waves in General Relativity

2021 ◽  
Vol 9 (12) ◽  
pp. 981-988
Author(s):  
Dr. Shailendra Kumar Srivastava
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Vast Number ◽  
Gravitational Fields ◽  
Time Singularities ◽  
Linearized Theory ◽  
High Degree

Abstract: For many years after Einstein proposed his general theory of relativity, only a few exact solutions were known. Today the situation is completely different, and we now have a vast number of such solutions. However, very few are well understood in the sense that they can be clearly interpreted as the fields of real physical sources. The obvious exceptions are the Schwarzschild and Kerr solutions. These have been very thoroughly analysed, and clearly describe the gravitational fields surrounding static and rotating black holes respectively. In practice, one of the great difficulties of relating the particular features of general relativity to real physical problems, arises from the high degree of non-linearity of the field equations. Although the linearized theory has been used in some applications, its use is severely limited. Many of the most interesting properties of space-time, such as the occurrence of singularities, are consequences of the non-linearity of the equations. Keywords: General Relativity , Space-Time, Singularities, Non-linearity of the Equations.

scholarly journals Mechanics of spacetime — A Solid Mechanics perspective on the theory of General Relativity

2018 ◽  
Vol 27 (08) ◽  
pp. 1850083 ◽  
Author(s):  
T. G. Tenev ◽  
M. F. Horstemeyer
Keyword(s):  
General Relativity ◽  
Free Space ◽  
Elastic Moduli ◽  
Solid Mechanics ◽  
Physical Space ◽  
Gravitational Acceleration ◽  
Field Equations ◽  
Gravitational Fields ◽  
Small Strains ◽  
Strain Stress

We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the “cosmic fabric” and spacetime with the fabric’s worldvolume. Using a Lagrangian formulation, we show that the fabric’s behavior as derived from Hooke’s Law is analogous to that of spacetime per the Field Equations of General Relativity (GR). The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric’s Lagrangian outside of inclusions is shown to have the same form as the Einstein–Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves and the energy density of free space. By introducing a mechanical analogy of GR, we enable the application of Solid Mechanics tools to address problems in Cosmology.

scholarly journals The Geometrization of Maxwell’s Equations and the Emergence of Gravity

2021 ◽  
Author(s):  
Raymond Beach
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Curvature Tensor ◽  
Maxwell Equations ◽  
Classical Field Theory ◽  
Field Equations ◽  
Gravitational Fields ◽  
All Solutions ◽  
Maxwell Tensor

A recently proposed classical field theory in which Maxwell’s equations are replaced by an equation that couples the Maxwell tensor to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor provides a succinct framework for the classical Maxwell equations which are left intact as a derivable consequence. Beyond providing a basis for the classical Maxwell equations, the coupling of the Riemann-Christoffel curvature tensor to the Maxwell tensor leads to the emergence of gravity, with all solutions of the proposed theory also being solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Both electromagnetic and gravitational phenomena are put an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions with those of the classical Maxwell and Einstein field equations is emphasized throughout. Unique to the proposed theory and based on specific solutions are the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, and the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity. Finally, a method for quantizing the charge, mass, and angular momentum of particle-like solutions as well as the possibility of superluminal transport of specific curvature related quantities is conjectured.

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