Gravitational Radiation Energy Research Articles

An experiment to measure electromagnetic memory

Abstract We describe an experiment to measure the electromagnetic analog of gravitational wave memory, the so-called electromagnetic (EM) memory. Whereas gravitational wave memory is a residual displacement of test masses, EM memory is a residual velocity (i.e. kick) of test charges. The source of gravitational wave memory is energy that is not confined to any bounded spatial region: in the case of binary black hole mergers the emitted energy of gravitational radiation as well as the recoil energy of the final black hole. Similarly, EM memory requires a source whose charges are not confined to any bounded spatial region. While particle beams can provide unbounded charges, their currents are too small to be practical for such an experiment. Instead we propose a short microwave pulse applied to the center of a long dipole antenna. In this way the measurement of the kick can be done quickly enough that the finite size of the antenna does not come into play and it acts for our purposes the same as if it were an infinite antenna.

Energy of gravitational radiation and the background energy of the space-time

We address the issue of gravitational radiation in the context of the Bondi-Sachs space-time, and consider the expression for the gravitational energy of the radiation obtained in the realm of the teleparallel equivalent of general relativity (TEGR). This expression is independent of the radial distance (i.e., of powers of 1/r) and depends exclusively on the functions c(u,θ,ϕ) and d(u,θ,ϕ), which yield the news functions (u is the retarded time, u=t−r). We investigate the mathematical and physical features of this energy expression in the simpler framework of axial symmetry. Once a burst of gravitational radiation takes place in a self gravitating system, that leads to a loss of the Bondi mass, gravitational radiation is emitted throughout the whole space-time. The existence and presence of this radiation in the background structure of the space-time is consistent with the analysis developed by Papapetrou, and Hallidy and Janis, who found no proof that a gravitational system that emits a burst of gravitational radiation is preceded and followed by two stationary gravitational field configurations, namely, it seems that it is impossible for a gravitational system, which is initially stationary, to return to a stationary state after emitting a burst of axially symmetric gravitational radiation, in which case the space-time is not even asymptotically stationary. Therefore, it is plausible that the gravitational energy of radiation is present in the background structure of the space-time, and this is the energy predicted in the TEGR. This analysis leads us to conjecture that the noise detected in the large terrestrial gravitational wave observatories is intrinsically related to the background gravitational radiation.

A viable relativistic scalar theory of gravitation

We build a self-consistent relativistic scalar theory of gravitation on a flat Minkowski spacetime from a general field Lagrangian. It is shown that, for parameters that satisfy the equivalence principle, this theory predicts the same outcome as general relativity (GR) for every classical solar-system test. This theory also admits gravitational waves that propagate at the speed of light, and the gravitational radiation energy loss in a binary system is shown to be very similar to the GR prediction. We then analyze the strong gravity regime of the theory for a spherically symmetric configuration and find that there is an effective ‘singularity’ near the Schwarzschild radius. The main goal of this work is to show that, contrary to what is commonly believed, there are relativistic scalar theories of gravitation defined on a Minkowski spacetime that are not ruled out by the classical solar system tests of GR.

Generalization of the quadrupole formula for the energy of gravitational radiation in de Sitter spacetime

We study gravitational radiation produced by time changing matter source in de Sitter spacetime. We consider a cosmological Killing horizon instead of the conformal boundary used in the radiation theory in the Minkowski spacetime. The energy of the radiation passing through the horizon is derived. Our result takes the form of a generalized quadruple formula expressed in terms of the mass and pressure quadruple moments and is written explicitly up to the first order in $\sqrt{\Lambda}$. The zeroth order term recovers the famous Einstein's quadruple formula obtained for the perturbed Minkowski spacetime, whereas the first order term is a new correction.

The Process of Gravity

Fascinated people from the dawn of history, gravity is not understood, still. Here, we suggest that gravity is a result of a process in the material: (1) Gravitational photons are produced by all atoms that exist in nonzero temperature and or interact with radiation, similar to black body radiation. (2) Then, these photons move in the material. The electromagnetic properties of the gravitational photons and the structure of the object cause the photons’ trajectories to bend. (3) Such trajectories generate a force pointing to the center of mass of the object, due to the circular motion and the electromagnetic properties of the gravitational photons. These trajectories are radiated outwards, as in antennae, although at a much slower rate, due to that force. So basically gravity is a simple process (as black body radiation), just a sort of generalized radiation pressure due to the process of gravity in the material, resulting in antenna like radiation emission, of these unique electromagnetic waves that are pressed towards the radiating object center of mass during their circular motion in the object. Going beyond the dynamical model, we identify various possible forms of the gravitational photons, and their general invariant properties. With this theory, we (1) explain various unexplained phenomena that are related to gravity, yet also suggest (2) method and apparatus for gravity shielding, and (3) gravitational radiation energy cultivation. This theory can form the missing part for the “theory of everything”.

Soft gravitational radiation from multi-body collisions

We derive a universal expression for the gravitational radiation energy spectrum dEGW/dω at sub-leading order emitted from a generic gravitational hard scattering of multi-particles or multi-bodies. Our result includes all mathcal{O} (ω) corrections to the gravitational radiation flux from a generic 2 → N collision, in both the cases of massless and massive particles/bodies. We also show the dependence of the radiation energy flux by the quantum spin in case of particle collisions. Then, we consider the specific case of a gravitational elastic scattering of two massive bodies, i.e. m + M → m + M with m, M the masses of the two bodies respectively. We demonstrate that in this case all mathcal{O} (ω) contributions to the energy flux exactly cancel each others. Nevertheless, we also show that, for a 2 → 2 inelastic scattering, the inclusion of sub-leading soft gravitons leads to a not zero radiation flux, having a simple expression in certain asymptotic regimes. Our results can be applied to the case of Black Hole collisions with possible testable implications in gravitational waves physics.

Gravitons into Gravitational Field

The problems connected to propagation of a gravitational field are considered. The constant homogeneous gravitational field is investigated. The law of electromagnetic radiation frequency change in this gravitational field is shown. On the basis of the solution of the Einstein’s equation for a weak gravitational field, the flux of gravitational radiation energy from system of cooperating masses is found. The equation for gravitational waves is found. On the basis of refusal from a stresses tensor into energy-impulse tensor and use of a quantum gravitational eikonal, the quantum form of the energy-impulse tensor in Einstein’s equation is found. The equation for a graviton propagating in a gravitational field of a double star is found. Resonant interaction of a graviton and a gravitational field of a double star are investigated. It is shown that such interaction allows registering the gravitons.

The cosmological constant and the energy of gravitational radiation

We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $\Lambda \in {\mathbb R}^*$, generalising the definition of Trautman and Bondi for $\Lambda=0$. We show that our definition reduces to some standard definitions in several situations. We establish a balance formula linking the characteristic mass and a suitably defined renormalised volume of the null hypersurface, generalising the positivity identity of one of us (PTC) and Paetz proved when $\Lambda=0$.

Bondi–Sachs energy-momentum and the energy of gravitational radiation

We construct the gravitational energy-momentum of the Bondi-Sachs space-time, in the famework of the teleparallel equivalent of general relativity (TEGR). The Bondi-Sachs line element describes gravitational radiation in the asymptotic region of the space-time, and is determined by the mass aspect and by two functions, $c$ and $d$, that yield the news functions, which are interpreted as the radiating degrees of freedom of the gravitational field. The standard expression for the Bondi-Sachs energy-momentum is constructed in terms of the mass aspect only. The expression that we obtain in the context of the TEGR is given by the standard expression, which represents the gravitational energy of the source, plus a new term that is determined by the two functions $c$ and $d$. We interpret this new term as the energy of gravitational radiation.

Gravitational Radiation from Keplerian Binary with Oscillating Orbital Plane

The gravitational radiation from two point masses in Keplerian circular or elliptic orbit is calculated with the assumption that the orbital plane of the binary undergoes small oscillation about the equilibrium x-y plane. This problem is simplification of a physically possible orbit where one of the point masses is spinning whereby the spin-orbit force drives the orbital plane to wobble in a complicated manner. It is shown that the total energy of gravitational radiation emitted by the binary in this case is greater than the energy emitted when the binary orbit is fixed in the x-y plane. The results presented are in fact a generalization of the classic results of Landau and Lifshitz. Keywords: Gravitational wave; Energy; Binary; Oscillating orbit.©2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved.

Energy of gravitational radiation in plane-symmetric space-times

Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a nonlinear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasilocal energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.

Oscillation damping of chiral string loops

Chiral cosmic string loop tends to the stationary (vorton) configuration due to the energy loss into the gravitational and electromagnetic radiation. We describe the asymptotic behaviour of near stationary chiral loops and their fading to vortons. General limits on the gravitational and electromagnetic energy losses by near stationary chiral loops are found. For these loops we estimate the oscillation damping time. We present solvable examples of gravitational radiation energy loss by some chiral loop configurations. The analytical dependence of string energy with time is found in the case of the chiral ring with small amplitude radial oscillations.

Mass correction and gravitational energy radiation in black-hole perturbation theory

Using second-order black-hole perturbation theory, we show that the difference between the ADM mass and the final black-hole mass, computed to the lowest significant order, is equal, to the same order, to the total gravitational radiation energy, obtained by applying the Landau - Lifschitz (pseudotensor) equation to the first-order perturbation. This result may be considered as a consistency check for the theory.

Gravitational waves generated by the vacuum stress.

We show that the $\frac{1}{\ensuremath{\square}}$, $\ensuremath{\square}\ensuremath{\rightarrow}\ensuremath{-}0$ asymptotic terms discovered in the one-loop vertices of quantum gravitating fields result in a new effect: a generation of the gravitational waves from the vacuum. This is an effect of the backreaction of the vacuum stress on the metric. A new method is proposed for calculating the energy of gravitational radiation that can be used in classical problems as well.

The new formula for gravitational radiation energy loss Applications to the axisymmetric two-body problem and the binary pulsar

view Abstract Citations (3) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The New Formula for Gravitational Radiation Energy Loss: Applications to the Axisymmetric Two-Body Problem and the Binary Pulsar Cooperstock, F. I. ; Lim, P. H. Abstract By accounting for nonlinearities and applying the Gauss theorem for retarded functions, the formula for gravitational radiation energy loss in general relativity is developed. This replaces the quadrupole formula, while clarifying the evident minimal domain of validity of the quadrupole formula. The new formula is considered in detail for the axisymmetric two-body problem with the conventional equation of state, epsilon = epsilon (Rho), where the nonlinear contributions are shown to cancel and the time-retardation contributions vanish individually. An order-of-magnitude analysis is performed for the binary pulsar, whereby it is found that both types of new contributions have the potential to compete with the quadrupole term. Publication: The Astrophysical Journal Pub Date: May 1986 DOI: 10.1086/164205 Bibcode: 1986ApJ...304..671C Keywords: Axisymmetric Bodies; Binary Stars; Gravitational Waves; Pulsars; Relativity; Two Body Problem; Computational Astrophysics; Energy Dissipation; Equations Of State; Gauss Equation; Quadrupoles; Astrophysics; GRAVITATION; PULSARS; RADIATION MECHANISMS; RELATIVITY; STARS: BINARIES full text sources ADS | data products SIMBAD (1)

The new formula for gravitational-radiation energy loss and the axially symmetric two-body problem

We present the new formula for gravitational-radiation energy loss that replaces the familiar quadrupole formula. The new formula helps to clarify why the quadrupole formula works when it does. The origin of the correction tensor is discussed and then applied to the axially symmetric two-body problem. With the conventional equation of state, ε = ε(P), the correction tensor vanishes and the radiation is that of the bulk-motion quadrupole formula. This is to be compared with our earlier result with an unconventional equation of state giving more radiation and with that of critics claiming dominant radiation via internal motions with the quadrupole formula. An order-of-magnitude calculation is performed for a binary system, where it is found that there is the potential for contributions from nonlinear terms to be as significant as those from the linear terms after(Gm/α)−5/6 orbits. This occurs after ~102 years for the binary pulsar PSR1913 + 16.

New formula for gravitational radiation energy loss in general relativity.

Field contributions and the Gauss theorem for retarded functions lead to a new formula for gravitational radiation energy loss. It clarifies the applicability of the quadrupole formula for systems with ${\mathrm{T}}^{\mathrm{ik}}$-dominated motion. Applied to the axially symmetric two-body problem with equation of state \ensuremath{\epsilon}=\ensuremath{\epsilon}(P) for short free-fall times, the new formula yields the bulk-motion quadrupole-formula result. This contrasts our earlier larger flux with unconventional equation of state and that of critics claiming a quadrupole formula flux from internal motions. An order of magnitude estimate yields potential corrections of quadrupole formula size after \ensuremath{\sim}${10}^{2}$ yr for the binary pulsar.

Witten's expression for gravitational energy

The origin and physical interpretation of Witten's integral expression for gravitational energy is examined. It is shown that this expression (including nonzero ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$) arises naturally from a Hamiltonian treatment of classical supergravity, without consideration of the quantum theory. In addition, this expression is evaluated explicitly in several examples. It is found that the individual terms do not have a simple physical interpretation. New integral expressions are then introduced in which the gravitational energy divides naturally into a conformally invariant and nonconformally invariant contribution. It is argued that in certain circumstances these contributions can be interpreted as the gravitational radiation energy and total binding energy for strongly gravitating systems.

Axially symmetric gravitational two-body problem of Cooperstock, Lim, and Hobill

Cooperstock, Lim, and Hobill have constructed and analyzed a model spacetime describing the head-on free-fall from rest of two fluid balls under their mutual gravitational attraction. These authors find a gravitational radiation energy flux having a different dependence on the parameters of the problem than would be expected on the basis of the quadrupole formula. We show that this dependence is due to their having incorrectly solved Einstein's gravitational field equations. The correct solution is consistent with the quadrupole formula.

Gravitational radiation induced by a particle falling along the Z-axis into a Kerr black hole

We have computed the spectrum and the energy of gravitational radiation induced by a test particle of mass μ falling along the z-axis into a Kerr black hole of mass M(⪢ μ) and angular momentum Ma( a < M). It is found that the total energy radiated is 0.0170 0.0170 μc 2 μM when α = 0.99 M, which is 1.65 times larger than that when α = 0, i.e., the Schwarzschild black hole case.