Gravitational Wave Energy Research Articles

Gravitational radiation from realistic relativistic stars: Odd-parity fluid perturbations.

Odd-parity gravitational perturbations of a spherically symmetric background are studied in the linearized Einstein theory. A variety of collapse models, based on a May-White hydrodynamic code, are investigated, simulating dust collapse and stellar core collapse typical of type-II supernova models. Numerical results are presented, showing that in this linearized problem a typical core collapse may radiate up to ${10}^{\mathrm{\ensuremath{-}}7}$ ${\mathrm{Mc}}^{2}$ in gravitational-wave energy.

Gravitational-wave emission from rotating gravitational collapse.

We present results for the gravitational radiation from the collapse to a black hole of rotating relativistic polytropes. The wave form closely resembles that emitted by a test particle infalling into a black hole, but the amplitude is reduced and opposite in sign. Less than 0.07% of the star's mass is converted to gravitational-wave energy. With sufficient rotation, the star bounces and no black hole forms. These results were obtained with a fully general-relativistic computer code that evolves rotating axisymmetric configurations and directly computes their gravitational-radiation emission.

Absorption of gravitational energy by a viscous compressible fluid in a curved spacetime

view Abstract Citations (8) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Absorption of gravitational energy by a viscous compressible fluid in a curved spacetime Papadopoulos, D. ; Esposito, F. P. Abstract The response of a viscous, compressible fluid in a curved spacetime to an incident gravitational wave is calculated. This response consists of a sound wave and a shear wave, and the absorption cross section is evaluated in terms of these waves. While the cross section is small for Newtonian velocities, it does increase as the speed of sound increases. Thus, the more rigid the fluid becomes, i.e., the higher the sound velocity, the more the fluid absorbs the energy of the gravitational wave, suggesting that in some circumstances not much gravitational wave energy escapes from the environment of the radiating object. Publication: The Astrophysical Journal Pub Date: May 1985 DOI: 10.1086/163163 Bibcode: 1985ApJ...292..330P Keywords: Astronomical Models; Compressible Fluids; Gravitational Waves; Magnetohydrodynamics; Relativity; Viscous Fluids; Absorption Cross Sections; Energy Absorption; Equations Of Motion; S Waves; Sound Waves; Space-Time Functions; Astrophysics full text sources ADS |

Gravitational Radiation from a Particle with Orbital Angular Momentum Plunging into a Kerr Black Hole

Using the Sasaki-Nakamura equation, we have computed the energy, linear and angular momentum of the gravitational radiation induced by a particle of mass /1 and angular momentum /1L z plunging in an equatorial plane into a Kerr black hole of mass M(~/1) and angular momentum Ma. It is found that the total energy LlE (/1/ M )/1C 2 is emitted by the particle with sufficient large orbital angular momentum. For the same value of ILzl, a corotating particle emits more energy than a counter-rotating one. We have also calculated the energy from a rotating ring plunging into a Kerr black hole. In this case, we have found' that a corotating ring emits less gravitational energy than a counter-rotating one for the same ILzl. The maximum of the linear momentum is 6 x 102 (/1/ M )/1C, which suggests the recoil velocity of the coalesced black hole is 160 km/s for /1=0.1 M. Since Davis et al. l ) first calculated the energy by a particle of mass f..l falling into a Schwarzschild black hole of mass M (~f..l), many calculations have been performed for the energy, linear and angular momentum radiated by a particle or particles falling into a black hole. 2 )-4) However, for a Kerr black hole case, before the discovery of the Sasaki­ Nakamura equation,5) there existed only the work-by Detweiler 6 ) for the luminosity from a particle in a circular orbit. The Teukolsky equation,7) which governs the perturbations of the Kerr black hole, has a long range potential and divergent source terms, which prevented us from the actual numerical calculations in generic cases. Sasaki and Nakamura got rid of these difficulties by discovering a new transformation. Using the Sasaki -Nakamura equation, Nakamura and Sasaki 5),8) first calculated the energy from a particle falling along the symmetry axis of the Kerr black hole. Nakamura and Haugan 9 ) calculated the linear momentum for the same case. The present authors lO ) have calculated the gravitational radiation from a particle of mass f..l with zero orbital angular momentum plunging in the equatorial plane (e = 7[/ 2 plane) into a Kerr black hole of mass M(~f..l) and angular momentum Ma. They confirmed the quasi-normal modes ll ) of the ,Kerr black hole. The energy for a=O.99M is 4.45xIO- 2 (f..l 2 /M)c2 which is 4.27 times larger than that for a=O case. In this paper, we examine more general cases than those considered in the previous papers. We calculate tpe energy, momentum and angular momentum of gravitational waves radiated, when a test particle of mass f..l with the orbital angular momentum f..lLz plunges in the equatorial plane into a Kerr black hole of mass M(~f..l) and angular momentum Ma. In §2, we show our mathematical formalism briefly. We will use the Sasaki-Nakamura equation instead of the Teukolsky equation. In §3, the numerical results are given. Section 4 is devoted to some discussion and astrophysical implications of the numerical results. Throughout this paper, we will represent a Kerr black hole by Boyer-Lindquist coordinates with (t, r, e, ¢) and use units of c = G = M = 1.

Energy, Momentum and Angular Momentum of Gravitational Waves Induced by a Particle Plunging into a Schwarzschild Black Hole

Energy, Momentum and Angular Momentum of Gravitational Waves Induced by a Particle Plunging into a Schwarzschild Black Hole

On the energy of gravitational waves in Einstein's theory of gravitation

On the energy of gravitational waves in Einstein's theory of gravitation

Gravitational Radiation and Observational Cosmology

view Abstract Citations (5) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gravitational Radiation and Observational Cosmology Isaacson, Richard A. ; Winicour, Jeffrey Abstract Recent observations by Weber indicate that a high flux of gravitational radiation is now being generated within the Galaxy. Assuming our environment to be typical, we must expect all galaxies to behave similarly, leading to large total amounts of gravitational wave energy in the cosmos. We have constructed an evolutionary model for the generation of gravitational radiation subsequent to galaxy formation and examined how the dynamics of the Universe are affected by the conversion of matter into radiation over a time scale of several billion years. If our Galaxy now converts more than 100 M0 per year into gravitational waves, we find that this radiation can play as important a role as matter in the evolution of the Universe. We use the latest values of the Hubble constant and deceleration parameter and find that the lifetime of a radiating cosmology is shortened from the Friedmann value to lie in the range 11 to 14 billion years. Subject headings: cosmology - gravitation Publication: The Astrophysical Journal Pub Date: August 1973 DOI: 10.1086/152302 Bibcode: 1973ApJ...184...49I full text sources ADS |

Energy of Gravitational Shock Waves

A model of a gravitational shock wave is developed using the null hypersurface approach to the initial value problem. Interior to the shock front is a flat Minkowski region. This is joined to a shear-free but curved exterior. The geometric properties of the shock front determine the physical properties of the wave. The gravitational energy measured at null infinity is a functional of the 2-geometry of the shock front. The positive energy conjecture reduces to a simple statement concerning the geometry of 2-surfaces. Explicit numerical calculations carried out for various 2-surfaces have led to positive energy. However, no inequality is known to show that the energy is positive for all 2-surfaces.

ON THE ADJUSTMENT TOWARD BALANCE IN PRIMITIVE EQUATION WEATHER PREDICTION MODELS

A formal solution of a linear geostrophic adjustment problem for the baroclinic atmosphere is derived. On the basis of this solution, the adjustment toward balance in primitive equation models is discussed with respect to its dependence on scale in space and time, and also with respect to the processes by which the adjustment takes place, that is, the damping and dispersion of the gravitational wave energy. Throughout the discussion, the effect of finite-difference approximations is considered. Finally, a numerical experiment is described that illustrates some of the results from the theoretical investigations.

Laboratory simulation of waves in an ice floe

An attempt is made to determine whether the complex natural phenomenon of the interaction of pack ice and ocean waves can be studied effectively in a laboratory model. Owing to the large number of variables involved in such a study, this paper considers mainly the relatively easier problem of the study of the dynamic behavior of ocean waves and an ice floe. Ocean waves and ice floes are simulated by waves in a laboratory channel and by thin floating sheets of polyethylene. From theoretical considerations, the phase velocity of waves through the sheet and the factors that influence wave reflection and transmission are developed. Phase velocity can be expressed as a function of the effective modulus of elasticity, density and thickness of polyethylene, the density of water, and the velocity of waves on a free water surface. Reflection and transmission depend on a number of dimensionless parameters, such as the ratio of sheet thickness to the incident wave height and the ratio of the elastic wave energy in the sheet to the incident gravitational wave energy. The reflection and transmission coefficients of the system and the phase velocity of waves propagating through the sheet are determined experimentally. A comparison of the theoretical predictions and results from model test indicates that a reasonable agreement exists between theory and experiment. Measurements of spectral energy density in open sea and results from model studies of this kind, which, however, take into account the patchiness of floes, may be applied to predict the attenuation experienced by waves that pass into pack ice. Values of effective viscosities determined from the simple model are applied to predict wave attenuation based on Robin's measurements in the south polar sea. The limitations of the model study are discussed.

On weak time-symmetric gravitational waves

The existence and the nature of the solutions of the initial value condition for the time-symmetric pure gravitational waves are investigated. It is shown that, corresponding to any nonsingular three-dimensional metric which is sufficiently close to the flat metric, there exists one and only one nonsingular solution of the initial value condition which is conformal to that metric. It is further shown that the energy of such gravitational waves is positive definite provided that the original metric is chosen sufficiently close to the flat metric.

Energy and Momentum of Cylindrical Gravitational Waves

Energy and Momentum of Cylindrical Gravitational Waves