scholarly journals The Method of Virtual Quanta and Gravitational Radiation

1974 ◽  
Vol 64 ◽  
pp. 16-16
Author(s):  
Richard A. Matzner ◽  
Yavuz Nutku
Keyword(s):  
Test Particle ◽  
Gravitational Radiation ◽  
Plane Waves ◽  
Test Body ◽  
Gravitational Energy ◽  
Fourier Component ◽  
Radiative Loss ◽  
Newtonian Type ◽  
Moving Particle

We extend the Weizsäcker-Williams method to the domain of gravitational encounters and correlate collision problems with the corresponding interaction of gravitational radiation. To an ultra-relativistic test particle the field of a Schwarzschild mass appears as a pulse of gravitational plane waves. We consider the scattering of each Fourier component, virtual quanta, by the Newtonian-type field of the test body. The scattered flux at infinity gives us the radiative loss of gravitational energy by a rapidly moving particle.

On the method of virtual quanta and gravitational radiation

1974 ◽  
Vol 336 (1606) ◽  
pp. 285-305 ◽  
Keyword(s):  
Gravitational Radiation ◽  
Frequency Component ◽  
Test Body ◽  
Point Particle ◽  
Gravitational Energy ◽  
Radiative Loss ◽  
Local Rest Frame ◽  
Newtonian Type ◽  
Moving Particle ◽  
Set Up

We extend the Weizsäeker-Williams method of virtual quanta to the domain of gravitational encounters and set up a correlation between collision problems and the corresponding interaction of gravitational radiation. In the local rest frame of a relativistic test particle the gravitational field of a Schwarzschild mass consists predominantly of a pulse of plane-fronted gravitational waves. We Fourier analyse this equivalent pulse and consider the scattering of each frequency component, virtual quanta, by the test body. The scattering by the long-range Newtonian-type field of a point particle is described by the analogue of the Rutherford cross-section. The escape of this scattered flux to infinity, suitably transformed, gives us the radiative loss of gravitational energy by a rapidly moving particle. The radiation spectrum and total energy radiated in a distant brehmsstrahlung encounter are computed as an example.

scholarly journals EXACT NONNULL WAVELIKE SOLUTIONS TO GRAVITY WITH QUADRATIC LAGRANGIANS

1994 ◽  
Vol 09 (02) ◽  
pp. 167-179 ◽  
Author(s):  
M.D. ROBERTS
Keyword(s):  
Gravitational Radiation ◽  
Riemann Tensor ◽  
Gravitational Energy ◽  
Cross Terms ◽  
Linearized Theory ◽  
Relationship Of ◽  
The Relationship ◽  
Poynting Vectors ◽  
Derivatives Of

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse N and the Riemann tensor takes the form [Formula: see text] thus these solutions depend on cross terms in the Riemann tensor and therefore complement linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitational energy Poynting vectors are constructed for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.

scholarly journals Improved Secular Stability Limits for Rotating White Dwarfs

1979 ◽  
Vol 53 ◽  
pp. 43-47
Author(s):  
R. H. Durisen ◽  
J. N. Imamura
Keyword(s):  
Kinetic Energy ◽  
Gravitational Radiation ◽  
Time Scale ◽  
White Dwarfs ◽  
Gravitational Energy ◽  
Dissipative Processes ◽  
Stability Limits ◽  
Special Case ◽  
Nonrotating Frame

In the special case of the Maclaurin spheroids, it has been known for some time that the m = 2 barlike modes become secularly unstable for t ≡ T/IWI ≥ 0.1376 where T is the total rotational kinetic energy and W is the total gravitational energy of the spheroid. “Secular” here means that the instability depends on dissipative processes and grows on a long dissipative time scale. In particular, the Dedekind-like bar mode, which has zero eigenfrequency at t = 0.1376 as viewed in the nonrotating frame, is unstable due to gravitational radiation (Chandrasekhar 1970).

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.

Does gravitational radiation impact the stellar habitable zone?

2020 ◽  
Vol 29 (11) ◽  
pp. 2041017
Author(s):  
J. A. S. Lima ◽  
R. C. Santos ◽  
J. V. Cunha ◽  
F. E. Silva ◽  
C. E. Pellicer
Keyword(s):  
Gravitational Radiation ◽  
Binary Systems ◽  
Analytical Formula ◽  
Gravitational Energy ◽  
Habitable Zone ◽  
Space Antenna ◽  
Substellar Objects ◽  
Optically Detected ◽  
Star Binary ◽  
Central Stars

Substellar objects of ultrashort periods (less than 50 min) orbiting central stars and many ultracompact star binary systems of even smaller periods (less than 10 min) have been optically detected in the last few years. Their gravitational luminosities can be of the same order or even much greater than their electromagnetic counterparts thereby also comprising a special class of targets for the Large Interferometer Space Antenna (LISA). In this paper, it is argued that the “gravitational illumination” of such systems may alter significantly the standard electromagnetic stellar habitable zone as long as a fraction of its gravitational energy is converted into heat. An analytical formula for the habitable zone is derived by assuming that the planet is simultaneously irradiated by electromagnetic and gravitational luminosities. The effect is quantified and some examples are discussed based on the available observations.

scholarly journals Gravitational waves in massive conformal gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
F. F. Faria
Keyword(s):  
Plane Wave ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Binary Systems ◽  
Plane Waves ◽  
Graviton Mass ◽  
Conformal Gravity ◽  
Physical Plane ◽  
Field Equations ◽  
Plane Wave Solution

Abstract First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in massive conformal gravity. We find that the theory with large graviton mass can reproduce the orbit of binaries by the emission of gravitational waves.

scholarly journals Gravitational energy of a noncommutative Vaidya black hole

2013 ◽  
Vol 91 (3) ◽  
pp. 242-245 ◽  
Author(s):  
S. Hamid Mehdipour
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Effective Mass ◽  
Test Particle ◽  
Mass Parameter ◽  
Naked Singularity ◽  
Gravitational Energy ◽  
Gravitational Mass ◽  
Vaidya Black Hole ◽  
Finite Distance

In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

scholarly journals Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 100
Author(s):  
José Wadih Maluf ◽  
Sérgio Ulhoa ◽  
Fernando Lessa Carneiro ◽  
Karlúcio H. C. Castello-Branco
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Energy Spectrum ◽  
Gravitational Radiation ◽  
Asymptotic Expression ◽  
Quasinormal Modes ◽  
Simple Expression ◽  
Gravitational Energy ◽  
Schwarzschild Black Hole ◽  
Constant Radius

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius r, in the region m<<r<<∞, where m is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers n and l that describe the quasinormal modes. In this sense, the energy perturbations are discretized. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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