A definition of the gravitational field inside matter

1980 ◽  
Vol 19 (3) ◽  
pp. 169-175 ◽  
Author(s):  
N. K. Kofinti
Keyword(s):  
Gravitational Field ◽  
Definition Of

scholarly journals WKB FORMALISM AND A LOWER LIMIT FOR THE ENERGY EIGENSTATES OF BOUND STATES FOR SOME POTENTIALS

2007 ◽  
Vol 22 (35) ◽  
pp. 2675-2687 ◽  
Author(s):  
LUIS F. BARRAGÁN-GIL ◽  
ABEL CAMACHO
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Lower Bound ◽  
Harmonic Oscillator ◽  
Approximation Method ◽  
Bound States ◽  
The Other ◽  
Homogeneous Gravitational Field ◽  
Definition Of ◽  
Ground Energy

In this work the conditions appearing in the so-called WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the textbooks on quantum mechanics, whereas the other is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the so-called Rayleigh–Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.

Formation of an expanded criteria base for managing the effectiveness of the most important elements of advanced space systems for monitoring the Earth's gravitational field

2021 ◽  
pp. 17-25
Author(s):  
Л.Г. Азаренко
Keyword(s):  
Gravitational Field ◽  
Space Systems ◽  
Earth’S Gravitational Field ◽  
Expanded Criteria ◽  
Definition Of

В статье рассматриваются подходы к формированию критериальной базы оценки эффективности при проектировании перспективных космических систем на примере космических систем мониторинга гравитационного поля Земли. Сформулированы основные требования к созданию критериальной базы. Дано определение критерия и обобщенного критерия эффективности применительно к элементам перспективных космических систем. Рассмотрены общие и частные критерии эффективности перспективных космических систем в зависимости от назначения конкретной системы (оборонного применения, гражданские, многоцелевые). The article considers approaches to the formation of a criteria base for evaluating the effectiveness of the design of advanced space systems on the example of space systems for monitoring the Earth's gravitational field. The main requirements for creating a criteria base are formulated. The definition of the criterion and the generalized criterion of efficiency in relation to the elements of advanced space systems is given. General and specific criteria for the effectiveness of advanced space systems are considered, depending on the purpose of a particular system (defense, civil, multi-purpose).

On the attractive force of the gravitational field in static space times

1970 ◽  
Vol 68 (1) ◽  
pp. 187-197 ◽  
Author(s):  
H. Müller zum Hagen
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Gravitational Force ◽  
Killing Vector ◽  
Attractive Force ◽  
Potential Surfaces ◽  
Asymptotically Flat ◽  
Definition Of ◽  
Meaningful Definition ◽  
Static Space

AbstractA static metric is considered. A meaningful definition of gravitational force is given and the potential, which is the norm of the Killing vector ξa, is studied. For the case that the metric is asymptotically flat, the following is shown: The equi-potential surfaces are closed 2-dimensional surfacesSlying in the rest space V3, which is the hypersurface orthogonal to ξa. All the surfacesSenclose matter, and the gravitational force points intoStowards the enclosed matter. A test particle starting atSwill be pulled into the domain bounded bySand will never leave this domain.

scholarly journals Unification of Gravity and Electromagnetism

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Mathematical Structure ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Field Equations ◽  
Mathematical Structures ◽  
Gravitational Field Equations ◽  
Definition Of ◽  
Two Sides

Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are representing by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure. Symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian

On the definition of the vacuum in the Gravitational field; the?vacuum

1977 ◽  
Vol 33 (1) ◽  
pp. 843-852 ◽  
Author(s):  
I. V. Volovich ◽  
V. A. Zagrebnov ◽  
V. P. Frolov
Keyword(s):  
Gravitational Field ◽  
Definition Of

Propagation of electromagnetic wave in gravitational field

2021 ◽  
Vol 34 (1) ◽  
pp. 89-96
Author(s):  
Yan Yi
Keyword(s):  
Electromagnetic Wave ◽  
Gravitational Field ◽  
Photoelectric Effect ◽  
Space Time ◽  
Propagation Path ◽  
Propagation Characteristics ◽  
Propagation Law ◽  
The Difference ◽  
Definition Of ◽  
Wave Properties

This paper is the third part of the induction theory of gravitational field. It mainly discusses some propagation characteristics of electromagnetic wave in the space-time constructed in the first paper [Y. Yi, Phys. Essays 33, 219 (2020)]. In this paper, a new definition of the basic properties of electromagnetic wave is given at first. Second, the photoelectric effect is explained by the new electromagnetic wave properties. Then, the propagation law of electromagnetic wave in space-time is discussed. Finally, the propagation law of electromagnetic wave in axisymmetric gravitational field is analyzed. According to the analysis in this paper, the propagation path of electromagnetic wave is unique in the spherical symmetric gravitational field, while the propagation path of electromagnetic wave in the axisymmetric gravitational field is related to the wavelength. This is the difference between the induction theory of gravitational field and the existing theory, which can be used to verify the theory of gravitational field induction.

scholarly journals The Erez–Rosen Solution Versus the Hartle–Thorne Solution

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1324
Author(s):  
Kuantay Boshkayev ◽  
Hernando Quevedo ◽  
Gulmira Nurbakyt ◽  
Algis Malybayev ◽  
Ainur Urazalina
Keyword(s):  
Gravitational Field ◽  
General Solution ◽  
Quadrupole Moment ◽  
Total Mass ◽  
Generalized Solution ◽  
Coordinate Transformations ◽  
Multipole Moments ◽  
Solution Versus ◽  
Definition Of ◽  
The Relationship

In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez–Rosen and the Hartle–Thorne solutions are particular solutions of a more general solution, the Zipoy–Voorhees transformation is applied to the exact Erez–Rosen metric in order to obtain a generalized solution in terms of the Zipoy–Voorhees parameter δ = 1 + s q . The Geroch–Hansen multipole moments of the generalized Erez–Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass m, quadrupole q and Zipoy–Voorhees δ parameters. The coordinate transformations between the metrics are found in the approximation of ∼q. It is shown that the Zipoy–Voorhees parameter is equal to δ = 1 - q with s = - 1 . This result is in agreement with previous results in the literature.

New definition of fluid exergy in a gravitational field

2010 ◽  
Vol 7 (6) ◽  
pp. 667
Author(s):  
Neven Ninic ◽  
Zdeslav Juric ◽  
Sandro Nizetic
Keyword(s):  
Gravitational Field ◽  
Definition Of

scholarly journals Field of Energy

2018 ◽  
Vol 14 (2) ◽  
pp. 5546-5553
Author(s):  
Armando Tomás Canero ◽  
Marco Armando Canero
Keyword(s):  
Gravitational Field ◽  
Dimensional Space ◽  
Classical Mechanics ◽  
The Other ◽  
Conservation Of Energy ◽  
Energy Field ◽  
Fundamental Properties ◽  
Temporal Dimensions ◽  
Definition Of ◽  
General Response

The study of physics requires the definition of general characteristics such as the so-called fundamental properties of space and time, which are homogeneity and isotropy. From the application of the homogeneity of time in the integral equations of the movement arises the theorem of the conservation of energy. That the parameter of variation be time leads to defining energy as scalar. Relativistic mechanics has shown that time is one of the dimensions of a tetra-dimensional space and, therefore, an event is projected in the spatial and temporal dimensions, this projection varies according to the reference system that is used. This indicates that equating time to a dimension of space, should be analyzed not only under the condition of homogeneity but also of the isotropy. This leads to analyzing energy as a vector. In classical mechanics, a body moving in a gravitational field its energy can be decomposed in two directions, one that remains constant, normal to the field, and the other that varies with gravity. This shows vector properties of energy. This study proposes a more general response through the energy field.

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