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.

IS THERE CLASSICAL SUPER-RADIANCE ON KERR-NEWMAN-ANTI-DE SITTER BLACK HOLES?

2002 ◽  
Vol 17 (20) ◽  
pp. 2782-2782
Author(s):  
ELIZABETH WINSTANLEY
Keyword(s):  
Black Holes ◽  
Boundary Conditions ◽  
Killing Vector ◽  
De Sitter ◽  
Transparent Boundary Conditions ◽  
Asymptotically Flat ◽  
Ads Black Holes ◽  
Definition Of ◽  
Conditions At Infinity ◽  
Positive Frequency

Since the formulation of the AdS/CFT correspondence 1, there has been great interest in space-times which are asymptotically anti-de Sitter, and the properties of the Kerr-Newman-anti-de Sitter (KN-AdS) space-time in various dimensions have been extensively studied 2. However, the properties of classical or quantum fields propagating on this background have not been widely studied, and, in particular, the question of whether super-radiance occurs has not been addressed. This is an important issue since a detailed understanding of classical super-radiance is necessary before tackling quantum field theory on rotating black hole geometries 3. We considered a classical scalar field on the KN-AdS background 4, and examined the form of the separated field modes. Given the structure of infinity in asymptotically anti-de Sitter space-times, we paid particular attention to the boundary conditions at infinity. Unlike the situation for asymptotically flat Kerr-Newman black holes 5, super-radiance is not inevitable. It depends partly on our choice of boundary condition at infinity. For reflective boundary conditions at infinity, there is no super-radiance. On the other hand, if we consider transparent boundary conditions at infinity, then the presence of super-radiance depends on our choice of positive frequency. For those KN-AdS black holes possessing a globally time-like Killing vector, then the natural definition of positive frequency implies that there are no super-radiant modes. For other KN-AdS black holes, then this same definition of positive frequency again leads to no super-radiance.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 395-409 ◽  
Author(s):  
Mayeul Arminjon
Keyword(s):  
Gravitational Field ◽  
Lorentz Force ◽  
Maxwell Equations ◽  
Gravitational Force ◽  
Continuous Medium ◽  
Pressure Force ◽  
Local Charge ◽  
Theory Of Gravitation ◽  
External Forces ◽  
Continuum Dynamics

AbstractAn alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Gravitational Force ◽  
Laser Interferometer ◽  
Speed Of Light ◽  
Gravitational Fields ◽  
Light Waves ◽  
Research Questions

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

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).

Dynamical black holes

2020 ◽  
pp. 312-336
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cauchy Data ◽  
Einstein Equations ◽  
Black Hole Spacetimes ◽  
Alternative Approaches ◽  
Definition Of ◽  
Meaningful Definition ◽  
Stability Results ◽  
Black Hole Solutions

In this chapter we review what is known about dynamical black hole-solutions of Einstein equations. We discuss the Robinson–Trautman black holes, with or without a cosmological constant. We review the Cauchy-data approach to the construction of black-hole spacetimes. We propose some alternative approaches to a meaningful definition of black hole in a dynamical spacetime, and we review the nonlinear stability results for black-hole solutions of vacuum Einstein equations.

scholarly journals On homogeneous and isotropic universe

2015 ◽  
Vol 30 (34) ◽  
pp. 1550186 ◽  
Author(s):  
M. O. Katanaev
Keyword(s):  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Killing Vector ◽  
Momentum Tensor ◽  
Killing Vector Fields ◽  
Full System ◽  
Independent Functions ◽  
Definition Of ◽  
Usual Scale ◽  
Matter Energy

We give a simple example of spacetime metric, illustrating that homogeneity and isotropy of space slices at all moments of time is not obligatory lifted to a full system of six Killing vector fields in spacetime, thus it cannot be interpreted as a symmetry of a four-dimensional metric. The metric depends on two arbitrary and independent functions of time. One of these functions is the usual scale factor. The second function cannot be removed by coordinate transformations. We prove that it must be equal to zero, if the metric satisfies Einstein’s equations and the matter energy–momentum tensor is homogeneous and isotropic. A new, equivalent, definition of homogeneous and isotropic spacetime is given.

scholarly journals Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1289 ◽  
Author(s):  
Valeriy Obukhov
Keyword(s):  
Test Particle ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Killing Vector ◽  
Field Equations ◽  
Tensor Fields ◽  
Charged Test Particle ◽  
Complete Sets ◽  
Charged Test ◽  
Hamilton Jacobi Equation

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity.

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