Orbits and rays in the gravitational field of a finite sphere according to the theory of A. N. Whitehead

1952 ◽  
Vol 211 (1106) ◽  
pp. 303-319 ◽  
Keyword(s):  
Gravitational Field ◽  
Continuous Distribution ◽  
Relativity Theory ◽  
Theory Of Relativity ◽  
Test Particles ◽  
Light Rays ◽  
Spherically Symmetric Distribution ◽  
Explicit Formulae ◽  
Finite Sphere ◽  
The Einstein Formula

The relativity theory of A. N. Whitehead permits one to calculate directly the gravitational field of a set of particles of assigned masses and arbitrary motions, and to investigate the orbits of test-particles and the paths of light rays in such a field. In this paper the hypothesis of Whitehead is extended to cover the case of a continuous distribution of matter; the field of a fixed sphere with a spherically symmetric distribution of matter is calculated and orbits and light rays discussed. Explicit formulae are obtained for advance of perihelion, angular velocity in a circular orbit, and deflexion of a light ray. The results differ only slightly from those of Einstein’s general theory of relativity by terms involving the distribution of matter in the sphere, except in the case of the deflexion of light, for which precisely the Einstein formula (depending only on total mass) is obtained.

scholarly journals Gravitational Fields of Conical Mass Distributions

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Chifu Ebenezer Ndikilar
Keyword(s):  
Gravitational Field ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Prolate Spheroidal ◽  
Radial Equation ◽  
Metric Tensor ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Oblate Spheroidal ◽  
Test Particles

The gravitational field of conical mass distributions is formulated using the general theory of relativity. The gravitational metric tensor is constructed and applied to the motion of test particles and photons in this gravitational field. The expression for gravitational time dilation is found to have the same form as that in spherical, oblate spheroidal, and prolate spheroidal gravitational fields and hence confirms an earlier assertion that this gravitational phenomena is invariant in form with various mass distributions. It is shown using the pure radial equation of motion that as a test particle moves closer to the conical mass distribution along the radial direction, its radial speed decreases.

MOTION AROUND A GLOBAL MONOPOLE

2000 ◽  
Vol 15 (06) ◽  
pp. 869-873
Author(s):  
A. BANERJEE ◽  
T. GHOSH
Keyword(s):  
Gravitational Field ◽  
Einstein Equations ◽  
Global Monopole ◽  
Test Particles ◽  
Light Rays ◽  
Bending Of Light

The motion of test particles and light rays in the perturbed gravitational field around a global monopole is studied. The metric of the monopole was previously obtained by solving the linearized semiclassical Einstein equations (Hiscock). The bending of light ray passing by such a monopole has contributions from the conical object as well as from the perturbed terms. The possibility of trapping particles in the perturbed gravitational field is also discussed.

On the matter of proving Euclidean fifth postulate and the origin of non-Euclidean geometries

2019 ◽  
Vol 950 (8) ◽  
pp. 2-11
Author(s):  
S.A. Tolchelnikova ◽  
K.N. Naumov
Keyword(s):  
Celestial Mechanics ◽  
Natural Philosophy ◽  
Relativity Theory ◽  
Theory Of Relativity ◽  
The Third ◽  
Stellar Astronomy ◽  
Spherical Surfaces ◽  
Mathematical System ◽  
Solar System Bodies ◽  
The Universe

The Euclidean geometry was developed as a mathematical system due to generalizing thousands years of measurements on the plane and spherical surfaces. The development of celestial mechanics and stellar astronomy confirmed its validity as mathematical principles of natural philosophy, in particular for studying the Solar System bodies’ and Galaxy stars motions. In the non-Euclidean geometries by Lobachevsky and Riemann, the third axiom of modern geometry manuals is substituted. We show that the third axiom of these manuals is a corollary of the Fifth Euclidean postulate. The idea of spherical, Riemannian space of the Universe and local curvatures of space, depending on body mass, was inculcated into celestial mechanics, astronomy and geodesy along with the theory of relativity. The mathematical apparatus of the relativity theory was created from immeasurable quantities

GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1678-1685 ◽  
Author(s):  
REZA TAVAKOL
Keyword(s):  
General Relativity ◽  
String Theory ◽  
Riemannian Geometry ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Spacetime Geometry ◽  
Test Particles ◽  
Light Rays ◽  
Recent Developments ◽  
Underlying Geometry

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more recent developments such as those in String theory, whereby Lorentz invariance is partially broken.

scholarly journals On the Support that the Special and General Theories of Relativity Provide for Rock’s Argument Concerning Induced Self-Motion and Vice Versa

2020 ◽  
Author(s):  
Douglas Michael Snyder
Keyword(s):  
Reference Frame ◽  
Empirical Work ◽  
Special Theory ◽  
The Other ◽  
Relativity Theory ◽  
Inertial Reference Frame ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Other Hand ◽  
Self Motion

Though Einstein and other physicists recognized the importance of an observer being at rest in an inertial reference frame for the special theory of relativity, the supporting psychological structures were not discussed much by physicists. On the other hand, Rock wrote of the factors involved in the perception of motion, including one’s own motion. Rock thus came to discuss issues of significance to relativity theory, apparently without any significant understanding of how his theory might be related to relativity theory. In this paper, connections between Rock’s theory on the perception of one’s own motion, as well as empirical work supporting it, and relativity theory are explored. Paper available at: https://arxiv.org/abs/physics/9908025v1 .

scholarly journals The relativity theory of plane waves

1926 ◽  
Vol 111 (757) ◽  
pp. 95-104 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Cumulative Effect ◽  
Relativity Theory ◽  
Transverse Waves ◽  
Propagation Of Light ◽  
Cumulative Change ◽  
The Waves

Weyl has shown that any gravitational wave of small amplitude may be regarded as the result of the superposition of waves of three types, viz.: (i) longitudinal-longitudinal; (ii) longitudinal-transverse; (iii) transverse-transverse. Eddington carried the matter much further by showing that waves of the first two types are spurious; they are “merely sinuosities in the co­ordinate system,” and they disappear on the adoption of an appropriate co-ordinate system. The only physically significant waves are transverse-transverse waves, and these are propagated with the velocity of light. He further considers electromagnetic waves and identifies light with a particular type of transverse-transverse wave. There is, however, a difficulty about the solution as left by Eddington. In its gravitational aspect light is not periodic. The gravitational potentials contain, in addition to periodic terms, an aperiodic term which increases without limit and which seems to indicate that light cannot be propagated indefinitely either in space or time. This is, of course, explained by noting that the propagation of light implies a transfer of energy, and that the consequent change in the distribution of energy will be reflected in a cumulative change in the gravitational field. But, if light cannot be propagated indefinitely, the fact itself is important, whatever be its explana­tion, for the propagation of light over very great distances is one of the primary facts which the relativity theory or any like theory must meet. In endeavouring to throw further light on this question, it seemed desirable to avoid the assumption that the amplitudes of the waves are small; terms neglected on this ground might well have a cumulative effect. All the solu­tions discussed in this paper are exact.

Bound orbits around modified Hayward black holes

2021 ◽  
Author(s):  
Bo Gao ◽  
Xue-Mei Deng
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Periodic Orbits ◽  
Kerr Black Hole ◽  
Periodic Oscillations ◽  
Test Particles ◽  
Spin Parameter ◽  
Bound Orbits

The neutral time-like particle’s bound orbits around modified Hayward black holes have been investigated. We find that both in the marginally bound orbits (MBO) and the innermost stable circular orbits (ISCO), the test particle’s radius and its angular momentum are all more sensitive to one of the parameters [Formula: see text]. Especially, modified Hayward black holes with [Formula: see text] could mimic the same ISCO radius around the Kerr black hole with the spin parameter up to [Formula: see text]. Small [Formula: see text] could mimic the ISCO of small-spinning test particles around Schwarzschild black holes. Meanwhile, rational (periodic) orbits around modified Hayward black holes have also been studied. The epicyclic frequencies of the quasi-circular motion around modified Hayward black holes are calculated and discussed with respect to the observed Quasi-periodic oscillations (QPOs) frequencies. Our results show that rational orbits around modified Hayward black holes have different values of the energy from the ones of Schwarzschild black holes. The epicyclic frequencies in modified Hayward black holes have different frequencies from Schwarzschild and Kerr ones. These might provide hints for distinguishing modified Hayward black holes from Schwarzschild and Kerr ones by using the dynamics of time-like particles around the strong gravitational field.

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