The Golden Dynamical Equation of Motion for Particles of Nonzero Rest Mass in Gravitational Fields.

2004 ◽  
Vol 17 (3) ◽  
pp. 295-300
Author(s):  
S. X. K. Howusu
Keyword(s):  
Dynamical Equation ◽  
Rest Mass ◽  
Equation Of Motion ◽  
Gravitational Fields

New conservation laws for zero rest-mass fields in asymptotically flat space-time

1968 ◽  
Vol 305 (1481) ◽  
pp. 175-204 ◽  
Keyword(s):  
Conservation Laws ◽  
Rest Mass ◽  
Power Series Expansion ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Maxwell Theory ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Higher Spin

Some recently discovered exact conservation laws for asymptotically flat gravitational fields are discussed in detail. The analogous conservation laws for zero rest-mass fields of arbitrary spin s = 0,½,1,...) in flat or asymptotically flat space-time are also considered and their connexion with a generalization of Kirchoff’s integral is pointed out. In flat space-time, an infinite hierarchy of such conservation laws exists for each spin value, but these have a somewhat trivial interpretation, describing the asymptotic incoming field (in fact giving the coefficients of a power series expansion of the incoming field). The Maxwell and linearized Einstein theories are analysed here particularly. In asymptotically flat space-time, only the first set of quantities of the hierarchy remain absolutely conserved. These are 4 s + 2 real quantities, for spin s , giving a D ( s , 0) representation of the Bondi-Metzner-Sachs group. But even for these quantities the simple interpretation in terms of incoming waves no longer holds good: it emerges from a study of the stationary gravitational fields that a contribution to the quantities involving the gravitational multipole structure of the field must also be present. Only the vacuum Einstein theory is analysed in this connexion here, the corresponding discussions of the Einstein-Maxwell theory (by Exton and the authors) and the Einstein-Maxwell-neutrino theory (by Exton) being given elsewhere. (A discussion of fields of higher spin in curved space-time along these lines would encounter the familiar difficulties first pointed out by Buchdahl.) One consequence of the discussion given here is that a stationary asymptotically flat gravitational field cannot become radiative and then stationary again after a finite time, except possibly if a certain (origin independent) quadratic combination of multipole moments returns to its original value. This indicates the existence of ‘tails’ to the outgoing waves (or back-scattered field),which destroys the stationary nature of the final field.

scholarly journals The Einstein–Infeld–Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles

2019 ◽  
Vol 28 (11) ◽  
pp. 1930017
Author(s):  
Michael K.-H. Kiessling ◽  
A. Shadi Tahvildar-Zadeh
Keyword(s):  
Initial Value Problem ◽  
Rest Mass ◽  
Relativity Theory ◽  
Field Energy ◽  
Gravitational Coupling ◽  
Field Equations ◽  
Initial Value ◽  
Classical Motion ◽  
Gravitational Fields ◽  
Charged Point

Einstein, Infeld and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This report identifies necessary conditions for a well-defined general-relativistic joint initial value problem of [Formula: see text] classical point charges and their electromagnetic and gravitational fields. Among them, in particular, is the requirement that the electromagnetic vacuum law guarantees a finite field energy–momentum of a point charge. This disqualifies the Maxwell(–Lorentz) law used by EIH. On the positive side, if the electromagnetic vacuum law of Bopp, Landé–Thomas and Podolsky (BLTP) is used, and the singularities equipped with a nonzero bare rest mass, then a joint initial value problem can be formulated in the spirit of the EIH proposal, and shown to be locally well-posed — in the special-relativistic zero-[Formula: see text] limit. With gravitational coupling (i.e. [Formula: see text]), though, changing Maxwell’s into the BLTP law and assigning a bare rest mass to the singularities is by itself not sufficient to obtain even a merely well-defined joint initial value problem: the gravitational coupling also needs to be changed, conceivably in the manner of Jordan and Brans–Dicke.

scholarly journals Kinematics, dynamics and the scale of time, III

1937 ◽  
Vol 159 (899) ◽  
pp. 526-547 ◽  
Keyword(s):  
External Force ◽  
Rest Mass ◽  
Equation Of Motion ◽  
Dynamical Time

1—In the first paper under the above title the relations between the t τ-dynamics and the τ-dynamics were developed for local events and small velocities, i. e. for | P | ≪ ct and | V | ≪ c . In the second paper the exact relativistic formulae were obtained for the motion of a free particle, and for the energy of any particle, free or constrained. The object of the present paper is to carry out the transformation of the equation of motion of a particle of "rest-mass" m under external force F, moving in the presence of the substratum, from tis expression in t -measures to its expression in τ-measures. It is supposed as before that the clocks of all fundamental observes in the substratum are re-graduated from kinematic time t to dynamical time τ, according to the formula τ = t 0 log( t / t 0 ) + t 0 . (1) The notation is that of former papers in the series.

scholarly journals Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Pinaki Patra ◽  
Md. Raju ◽  
Gargi Manna ◽  
Jyoti Prasad Saha
Keyword(s):  
Cosmological Model ◽  
Tangent Bundle ◽  
Dynamical Equation ◽  
Hamiltonian Formalism ◽  
Equation Of Motion ◽  
Scale Factor ◽  
Correct Equation ◽  
Higher Derivative ◽  
Alternative Approach ◽  
Tangent Manifold

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge-Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.

scholarly journals Electromagnetic field with induced massive term: Case with scalar field

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Yuri Rybakov ◽  
Georgi Shikin ◽  
Yuri Popov ◽  
Bijan Saha
Keyword(s):  
Electromagnetic Field ◽  
Field Equation ◽  
Scalar Field ◽  
Cosmological Model ◽  
Bianchi Type ◽  
Rest Mass ◽  
Additional Term ◽  
Equation Of Motion ◽  
Massless Scalar ◽  
Type I

AbstractWe consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.

scholarly journals Shielding the Gravitational Field in Space

2021 ◽  
pp. 1-3
Author(s):  
Yanbikov Vil'dyan Shavkyatovich ◽  
Keyword(s):  
Elementary Particle ◽  
Gravitational Field ◽  
Gravitational Waves ◽  
Cross Section ◽  
Rest Mass ◽  
Free Fall ◽  
Gravitational Fields ◽  
Gravitational Forces ◽  
The Galaxy ◽  
The Universe

The study presents a model for screening gravitational waves. fields of protons of the cosmos. Gravity shielding is based on a principle. An elementary particle with a rest mass. In free fall. Shields the gravitational fields in which it is located. In the above work the intensity of the gravitational field from the infinite cosmic field is determined half-spaces. The cross section of the proton shielding the gravitational field is determined. The radius of action of gravitational forces in space is calculated. The formula is obtained, which determines the distance to the galaxy by its " red " shift. Time calculated the life of a photon in space. The size of the visibility horizon of the universe is determined

The Einstein field equation

2021 ◽  
pp. 213-226
Author(s):  
Andrew M. Steane
Keyword(s):  
Field Theory ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Equation Of Motion ◽  
Energy Conditions ◽  
Gravitational Fields ◽  
Electromagnetic Field Theory ◽  
Stationary Conditions ◽  
Energy And Momentum ◽  
Insight Into

Various aspects of the Einstein field equation are presented. First the field equation is obtained by arguing that it is the simplest equation that respects the fundamental geometric insight into gravity. Then we consider whether the equation is stable, and introduce the weak energy and dominant energy conditions. The connection between inertial motion and the distant universe (Mach’s principle) is discussed. The equation of motion of matter is obtained from the field equation, and a comparison made with electromagnetic field theory. The energy and momentum of gravitational fields in stationary conditions is discussed, and the Komar energy obtained.

The Effect of Oil Entrapment in an Axial Piston Pump

1985 ◽  
Vol 107 (4) ◽  
pp. 246-251 ◽  
Author(s):  
S. J. Lin ◽  
A. Akers ◽  
G. Zeiger
Keyword(s):  
Pressure Distribution ◽  
Dynamical Equation ◽  
Control Volume ◽  
Equation Of Motion ◽  
Piston Pump ◽  
Axial Piston Pump ◽  
Angular Rotation ◽  
Instantaneous Pressure ◽  
Discharge Pressure ◽  
Axial Piston

Values of pressure caused by entrapment beneath a valve plate have been calculated. The technique used consists of the solution of the dynamical equation of motion in the piston control volume. Instantaneous and average values of torque have also been deduced from the pressure distribution. Plots have been constructed showing the effect of swashplate angle, pump angular rotation, discharge pressure, and entrapment angle upon instantaneous pressure, torque, and average torque for a typical axial piston pump.

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