scholarly journals Relativistic Reduction of Astrometric Observations at Points Level of Accuracy

1990 ◽  
Vol 141 ◽  
pp. 229-240
Author(s):  
V. A. Brumberg ◽  
S. A. Klioner ◽  
S. M. Kopejkin
Keyword(s):  
Gravitational Field ◽  
Flat Space ◽  
Satellite System ◽  
Relativity Theory ◽  
Position Vector ◽  
Geometric Optics ◽  
General Relativity Theory ◽  
Isotropic Geodesic ◽  
Stationary Gravitational Field ◽  
Relativistic Reduction

The framework of general relativity theory (GRT) is applied to the problem of reduction of high precision astrometric observations of the order of one microarcsecond. The equations of geometric optics for the non-stationary gravitational field of the Solar system have been deduced. Integration of the equations of geometric optics results in the isotropic geodesic line connecting the source of emission (a star, a quasar) and an observer. This permits to calculate the effects of relativistic aberration of light due to monopole and quadrupole components of the gravitational field of the Sun and the planets taking into account their motions and rotation. Transformations between the reference systems are used to calculate the light aberration occurring when passing from the satellite system to the geocentric system and from the geocentric system to the baryecntric system. The baryecntric components of the observed position vector reduced to the flat space-time are corrected, if necessary, for parallax and proper motion of a celestial object using the classical techniques of Euclidean geometry.

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

VAN DER WAALS FORCES IN CURVED SPACE AS A QUANTUM TOOL TO TEST GENERAL RELATIVITY THEORY

2005 ◽  
Vol 14 (06) ◽  
pp. 995-1008 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Experimental Test ◽  
Point Charge ◽  
Van Der Waals ◽  
Atom Interferometry ◽  
Relativity Theory ◽  
Spherically Symmetric ◽  
General Relativity Theory ◽  
Curved Space

It has been known shortly after the introduction of the general relativity theory that the electrostatic Coulomb potential of a point charge supported in a gravitational field is not spherically symmetric and becomes warped in curved space. Under ordinary laboratory conditions, this effect is quite small and has never been directly observed. Surprisingly, this distortion causes the appearance of a hitherto unknown, topologically complex non-central van der Waals force whose detection is well within range of existing trapped atom interferometry techniques. This will allow for an unexpected experimental test of gravity theory by means of quantum-electro-dynamical interatomic forces.

On the relativistic interpretation of astronomical observations

1959 ◽  
Vol 252 (1271) ◽  
pp. 476-487 ◽  
Keyword(s):  
Differential Equation ◽  
General Relativity ◽  
Apparent Motion ◽  
Flat Space ◽  
Frame Of Reference ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Astronomical Observations ◽  
Basic Ideas ◽  
Arbitrary Curvature

The basic ideas of apparent motion are formulated within the framework of general relativity theory. This requires the introduction of a dynamically meaningful frame of reference. A differential equation characterizing motion relative to this frame in a space of arbitrary curvature is formulated and its solutions for nearly flat space-time are obtained. These solutions are compared with the results of classical and special relativistic theory.

On The Motion of Particles in General Relativity Theory

1949 ◽  
Vol 1 (3) ◽  
pp. 209-241 ◽  
Author(s):  
A. Einstein ◽  
L. Infeld
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion ◽  
Relativity Theory ◽  
Fundamental Importance ◽  
Approximation Procedure ◽  
High Approximation ◽  
Field Equations ◽  
General Relativity Theory ◽  
First Time

The gravitational field manifests itself in the motion of bodies. Therefore the problem of determining the motion of such bodies from the field equations alone is of fundamental importance. This problem was solved for the first time some ten years ago and the equations of motion for two particles were then deduced [1]. A more general and simplified version of this problem was given shortly thereafter [2].Mr. Lewison pointed out to us, that from our approximation procedure, it does not follow that the field equations can be solved up to an arbitrarily high approximation. This is indeed true.

scholarly journals Nonlocal Gravitomagnetism

Universe ◽  
2019 ◽  
Vol 5 (9) ◽  
pp. 195 ◽  
Author(s):  
Mashhoon ◽  
Hehl
Keyword(s):  
Slow Motion ◽  
Weak Field ◽  
Relativity Theory ◽  
Current Status ◽  
General Relativity Theory ◽  
Differential Field ◽  
Gravitomagnetic Field ◽  
Motion Approximation ◽  
Theory Of Gravitation ◽  
Stationary Gravitational Field

We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocalgeneralization of Einstein’s theory of gravitation based on a certain analogy with the nonlocalelectrodynamics of media. Nonlocal gravity thus involves integro-differential field equationsand a causal constitutive kernel that should ultimately be determined from observational data.We consider the stationary gravitational field of an isolated rotating astronomical source in the linearapproximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG,we describe the gravitomagnetic field associated with the rotating source and compare our resultswith gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we brieflystudy the energy-momentum content of the GEM field in nonlocal gravity.

scholarly journals BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

2012 ◽  
Vol 21 (04) ◽  
pp. 1250037 ◽  
Author(s):  
DANIEL MÜLLER ◽  
JULIANO A. DE DEUS
Keyword(s):  
Numerical Solutions ◽  
Relativity Theory ◽  
De Sitter ◽  
General Relativity Theory ◽  
Spatial Metrics ◽  
Effective Gravity ◽  
Bianchi I ◽  
Quadratic Theory ◽  
Quadratic Gravity ◽  
Planck Time

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

scholarly journals Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Radiation Field ◽  
Relativity Theory ◽  
Covariant Theory ◽  
Spherically Symmetric ◽  
Theory U ◽  
General Relativity Theory ◽  
Infrared Limit ◽  
Symmetric Spacetime

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

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