scholarly journals Multipolar Test Body Equations of Motion in Generalized Gravity Theories

2015 ◽  
pp. 67-119 ◽  
Author(s):  
Yuri N. Obukhov ◽  
Dirk Puetzfeld
Keyword(s):  
Equations Of Motion ◽  
Test Body ◽  
Gravity Theories

Dynamics of extended bodies in general relativity. I. Momentum and angular momentum

1970 ◽  
Vol 314 (1519) ◽  
pp. 499-527 ◽  
Keyword(s):  
Equations Of Motion ◽  
Potential Energy Function ◽  
Test Body ◽  
The Body ◽  
External Fields ◽  
De Sitter ◽  
Extended Body ◽  
Rest Energy ◽  
Momentum Vector ◽  
De Sitter Universe

Definitions are proposed for the total momentum vector p α and spin tensor S αβ of an extended body in arbitrary gravitational and electromagnetic fields. These are based on the requirement that a symmetry of the external fields should imply conservation of a corresponding component of momentum and spin. The particular case of a test body in a de Sitter universe is considered in detail, and used to support the definition p β S αβ = 0 for the centre of mass. The total rest energy M is defined as the length of the momentum vector. Using equations of motion to be derived in subsequent papers on the basis of these definitions, the time dependence of M is studied, and shown to be expressible as the sum of two contributions, the change in a potential energy function ϕ and a term representing energy inductively absorbed, as in Bondi’s illustration of Tweedledum and Tweedledee. For a body satisfying certain conditions described as ‘dynamical rigidity’, there exists, for motion in arbitrary external fields, a mass constant m such that M = m + ½ S κ Ω κ + ϕ , where Ω k is the angular velocity of the body and S κ its spin vector.

scholarly journals Leaps and bounds towards scale separation

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
G. Bruno De Luca ◽  
Alessandro Tomasiello
Keyword(s):  
Ricci Tensor ◽  
Broad Class ◽  
Equations Of Motion ◽  
Internal Diameter ◽  
Warping Function ◽  
Local Behavior ◽  
Scale Separation ◽  
Planck Mass ◽  
Curvature Bound ◽  
Gravity Theories

Abstract In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

scholarly journals THE STABILITY OF QUASI-CIRCULAR ORBITS NEAR THE CENTRAL BODY

2020 ◽  
Vol 70 (2) ◽  
pp. 155-159
Author(s):  
М.Е. Abishev ◽  
◽  
С. Тоktarbay ◽  
А.Z. Таlkhat ◽  
A.Zh. Abylayeva ◽  
...  
Keyword(s):  
Circular Orbit ◽  
Stability Problem ◽  
Central Body ◽  
Equations Of Motion ◽  
Test Body ◽  
Circular Orbits ◽  
The Stability ◽  
The Hill

In the problem of relational bounded three bodies, the stability of quasicircular orbits close to the central body was investigated. In the case when it is not relational, the orbits of the test body can be described through the Hill surfaces. The location of the central body corresponds to the origin, the second body moves in a circular orbit that is around the central (first) body. The equations of motion of the problem of bounded, relational three bodies were investigated for circular orbits. Using these equations of relational motion, the stability problem of the relational quasicircular orbits of the test body in regions close to the central body was investigated.

scholarly journals A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM

2002 ◽  
Vol 11 (05) ◽  
pp. 781-787 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Slow Motion ◽  
Weak Field ◽  
Test Body ◽  
Angular Velocity Vector ◽  
Motion Approximation ◽  
General Relativistic

The well known general relativistic Lense–Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

scholarly journals Thermodynamic properties of modified gravity theories

2016 ◽  
Vol 13 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Kazuharu Bamba
Keyword(s):  
Thermodynamic Properties ◽  
Modified Gravity ◽  
Equations Of Motion ◽  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Modified Gravity Theories ◽  
Gravity Theories ◽  
Clausius Relation ◽  
The Universe

We review thermodynamic properties of modified gravity theories, such as [Formula: see text] gravity and [Formula: see text] gravity, where [Formula: see text] is the scalar curvature and [Formula: see text] is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in [Formula: see text] gravity. We show both equilibrium and nonequilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met, when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.

scholarly journals Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1408
Author(s):  
Taichiro Kugo
Keyword(s):  
Field Equation ◽  
Linear Combination ◽  
Source Term ◽  
Equations Of Motion ◽  
High Order Derivative ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Brs Symmetry ◽  
Noether Current ◽  
Global Translation

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s IOSp(8|8) choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term.

THE PAPAPETROU EQUATIONS AND MOTION OF A TEST BODY IN GRAVITATIONAL FIELD

1995 ◽  
Vol 04 (01) ◽  
pp. 69-78
Author(s):  
R.I. KHRAPKO
Keyword(s):  
Gravitational Field ◽  
Additional Condition ◽  
Evolution Equations ◽  
World Line ◽  
Equations Of Motion ◽  
Test Body ◽  
Particle Structure ◽  
Structure Equations

The Papapetrou equations for a dipole particle are criticized in favor of the evolution equations obtained by Dixon and Madore. It is concluded that an additional condition (Pirani, Dixon, Corinaldesi, etc.) which permits the calculation of a unique world line of a particle is a substitute for data of a particle structure. Equations of motion of an extended test body in terms of multipoles are presented.

scholarly journals GENERAL RELATIVITY, GRAVITATIONAL ENERGY AND SPIN–TWO FIELD

2007 ◽  
Vol 04 (01) ◽  
pp. 147-169
Author(s):  
LESZEK M. SOKOŁOWSKI
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Energy Density ◽  
Stress Tensor ◽  
Equations Of Motion ◽  
General Theorem ◽  
Gravitational Energy ◽  
Theory Approach ◽  
Gauge Invariant ◽  
Gravity Theories

In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field–theory approach to gravity? and iii) can a consistent theory of a gravitationally interacting spin–two field be developed at all? The connecting link to them is the concept of a fundamental classical spin–2 field. A linear spin–2 field introduced as a small perturbation of a Ricci–flat spacetime metric, is gauge invariant while its energy–momentum is gauge dependent. Furthermore, when coupled to gravity, the field reveals insurmountable inconsistencies in the resulting equations of motion. After discussing the inconsistencies of any coupling of the linear spin–2 field to gravity, I exhibit the origin of the fact that a gauge invariant field has the variational metric stress tensor which is gauge dependent. I give a general theorem explaining under what conditions a symmetry of a field Lagrangian becomes also the symmetry of the variational stress tensor. It is a conclusion of the theorem that any attempt to define gravitational energy density in the framework of a field theory of gravity must fail. Finally I make a very brief introduction to basic concepts of how a certain kind of a necessarily nonlinear spin–2 field arises in a natural way from vacuum nonlinear metric gravity theories (Lagrangian being any scalar function of Ricci tensor). This specific spin–2 field consistently interacts gravitationally and the theory of the field is promising.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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