scholarly journals MASSLESS SPINNING TEST PARTICLES IN ALGEBRAICALLY SPECIAL VACUUM SPACE–TIMES

2006 ◽  
Vol 15 (05) ◽  
pp. 737-758 ◽  
Author(s):  
DONATO BINI ◽  
CHRISTIAN CHERUBINI ◽  
ANDREA GERALICO ◽  
ROBERT T. JANTZEN
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Space Time ◽  
Null Direction ◽  
Massless Particles ◽  
Special Vacuum ◽  
Test Particles ◽  
Vacuum Space

The motion of massless spinning test particles is investigated using the Newman–Penrose formalism within the Mathisson–Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole reduction world line" lies along a principal null direction of an algebraically special vacuum space–time, the equations of motion can be explicitly integrated. Examples are given for some familiar space–times of this type in the interest of shedding some light on the consequences of this model.

Equations of motion in a generalized theory of gravitation

1981 ◽  
Vol 59 (11) ◽  
pp. 1723-1729 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Static Solution ◽  
Coupling Constant ◽  
Field Equations ◽  
Complete Space ◽  
Test Particles ◽  
Theory Of Gravitation ◽  
Definition Of ◽  
Universal Coupling

The problem of the motion of test particles is studied in a theory of gravitation based on a nonsymmetric gμν. According to the conservation laws the test particles can follow two kinds of geodesies, depending on the definition of a local inertial frame in the theory. One of these geodesies is nonmaximal and leads to a timelike and null world line complete space when a new parameter l, that occurs as a constant of integration in the spherically symmetric, static solution of the field equations, satisfies [Formula: see text]. In the theory, the parameter [Formula: see text] where N is the number of fermions in a system and a is a new universal coupling constant that satisfies [Formula: see text]. The physical implications of l and the associated conservation law of fermion number is discussed in detail.

Hertz─Bromwich─Debye─Whittaker─Penrose potentials in general relativity

1979 ◽  
Vol 367 (1731) ◽  
pp. 527-538 ◽  
Keyword(s):  
General Relativity ◽  
Scalar Potential ◽  
Space Time ◽  
Physical Interest ◽  
Gravitational Perturbations ◽  
Special Vacuum ◽  
Background Space ◽  
Explicit Formulae ◽  
Scalar Potentials ◽  
Vacuum Space

The problem of deriving scalar potentials governing electromagnetic and gravitational perturbations of vacuum space-times is discussed. For the case of an algebraically special vacuum background space-time, explicit formulae for all quantities of physical interest are given in terms of derivaties of the scalar potential.

scholarly journals THE PRINCIPLE OF LEAST ACTION FOR TEST PARTICLES IN A FOUR-DIMENSIONAL SPACE–TIME EMBEDDED IN 5D

2008 ◽  
Vol 23 (04) ◽  
pp. 249-259 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Dimensional Space ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Geodesic Equation ◽  
Space Time ◽  
Geodesic Motion ◽  
Least Action ◽  
Test Particles ◽  
Principle Of Least Action ◽  
Dimensional Space Time

It is well known that, in the five-dimensional scenario of braneworld and space–time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional reduction of the geodesic equation in 5D, without any reference to the test particle whatsoever. In this work we obtain the equation of motion in 4D directly from the principle of least action. So our main thrust is not the geometry but the particle observed in 4D. A clear physical picture emerges from our work. Specifically, that the deviation from the geodesic motion in 4D is due to the variation of the rest mass of a particle, which is induced by the scalar field in the 5D metric and the explicit dependence of the space–time metric on the extra coordinate. Thus, the principle of least action not only leads to the correct equations of motion, but also provides a concrete physical meaning for a number of algebraic quantities appearing in the geometrical reduction of the geodesic equation.

scholarly journals A brief review of E theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1630043 ◽  
Author(s):  
Peter West
Keyword(s):  
Infinite Number ◽  
Equations Of Motion ◽  
Space Time ◽  
Unified Theory ◽  
Dynamical Equations ◽  
Supergravity Theory ◽  
Maximal Supergravity ◽  
Abdus Salam ◽  
Strings And Branes ◽  
Time Lead

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

scholarly journals The Quadrantid Meteor Stream: Past, Present and Future

1980 ◽  
Vol 90 ◽  
pp. 153-156
Author(s):  
David W. Hughes ◽  
Iwan P. Williams ◽  
Carl D. Murray
Keyword(s):  
Solar System ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Meteor Stream ◽  
Eccentric Anomaly ◽  
Test Particles ◽  
The Future ◽  
Runge Kutta

At the present time the orbit of the Quadrantid meteor stream not only intersects the orbit of Earth but also passes very close to the orbit of the planet Jupiter. This causes considerable perturbations. In a series of three papers (1,2,3) the authors replaced the myriad of meteoroids in the stream by ten test particles set at equal intervals of eccentric anomaly around the orbit. The equations of motion of these particles in the solar system were solved using a standard fourth order Runge–Kutta technique with self–adjusting step lengths. The orbits of the test particles were output at ten year intervals going back from the present to the year 300 B.C. and forward into the future to the year A.D. 3780.

scholarly journals Elastic shocks in relativistic rigid rods and balls

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180858 ◽  
Author(s):  
João L. Costa ◽  
José Natário
Keyword(s):  
Free Boundary ◽  
Minkowski Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Space Time ◽  
Spherically Symmetric ◽  
Soft Phase ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We study the free boundary problem for the ‘hard phase’ material introduced by Christodoulou in (Christodoulou 1995 Arch. Ration. Mech. Anal. 130 , 343–400), both for rods in (1 + 1)-dimensional Minkowski space–time and for spherically symmetric balls in (3 + 1)-dimensional Minkowski space–time. Unlike Christodoulou, we do not consider a ‘soft phase’, and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.

Spinning strings of the Neveu-Schwarz-Ramond type in 3, 4, 6, and 10 space-time dimensions

1999 ◽  
Vol 77 (6) ◽  
pp. 427-446
Author(s):  
S B Phillips
Keyword(s):  
Degrees Of Freedom ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Physical Space ◽  
Space Time ◽  
Coordinate Space ◽  
Time Dimension ◽  
Light Cone Gauge ◽  
Fermionic Sector

A model of a spinning string with an internal coordinate index is proposed and studied. When the action for this model is taken to be diagonal in this internal coordinate space and quantized in the light-cone gauge it is found to be Lorentz covariant in four-dimensional space-time provided that the internal coordinate space is four dimensional.This combination of space-time dimension, D, and internal coordinate space dimension, N, is just one of four possible sets, the other three corresponding to D = 3, 6, and 10, precisely the same values for which it is possible to formulate Yang-Mills theories with simple supersymmetry. By comparing the number of propagating degrees of freedom at the zero-mass level in the open string bosonic and fermionic sectors it is found that a supersymmetric interpretation of this model is possible provided that all physical states in the bosonic sector have even G-parity and the ground-state spin or in the fermionic sector have positive chirality. A possible interpretation of the connection betweenthe N components of each of the D space-time coordinates is presentedon the basis that the space-time coordinates are scalars in the internal coordinate space. This interpretation would appear to be reasonable given the fact that the field variables in the Lagrangian density do not necessarily have to represent physically measurable quantities but can, instead, only represent physically measurable quantities when combined in some manner, the simplest of which being a linear combination. The Lagrangian density simply produces the equations of motion and the constraint equations for the independent variables, only linear combinations of which represent the four dimensions of physical space-time.PACS Nos.: 11.17.+y, 11.10.Qr, 1.30.Cp, 11.30.Pb

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