Flux Of Gravitational Radiation Research Articles

Classical soft graviton theorem rewritten

Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

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.

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

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.

Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order

Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the gravitational radiation flux dEGW/dω is re-derived and extended to order mathcal{O}left(omega right) and mathcal{O}left({omega}^2right) for arbitrary massless multi-particle collisions. The (angle-integrated, unpolarized) mathcal{O}left(omega right) correction to the flux turns out to be absent in the case of two-particle elastic collisions. The mathcal{O}left({omega}^2right) correction is instead non-vanishing and takes a simple general expression which is then applied to bremsstrahlung from two-particle elastic collisions. For a tree-level process the outcome is finite and consistent with expectations. Instead, if the tree-level form of the soft theorems is used at sub-sub-leading order even when the elastic amplitude needs an all-loop (eikonal) resummation, an unphysical infrared singularity occurs. Its origin can be traced to the infinite Coulomb phase of gravitational scattering in four dimensions. We briefly discuss how to get rid, in principle, of the unwanted divergences and indicate -without carrying out- a possible procedure to find the proper correction to the naive soft theorems. Nevertheless, if a simple recipe recently proposed for handling these divergences is adopted, we find surprisingly good agreement with results obtained independently via the eikonal approach to transplanckian-energy scattering at large (small) impact parameter (deflection angle), where such Coulomb divergences explicitly cancel out.

Energy–Momentum Tensor in the Relativistic Theory of Gravity

It has been shown that the following modification of the symmetric (Gilbert) total energy–momentum tensor (EMT) density $${t^{\mu v}} \to {t^{\mu v}} - \frac{{{m^2}}}{{16\pi G}}{\tilde \varphi ^{\mu v}}$$ leads to incorrect results in basic energetic calculations. It is pointed out that some attempts to prove the positive definiteness of the gravitational radiation flux in the RTG are based on the nonconservative energy–momentum tensor.

Tilted shear-free axially symmetric fluids

We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shear--free, irrotational, non--dissipative and purely electric, for the comoving congruence of observers, from the point of view of the tilted congruence. The vanishing of the magnetic part of the Weyl tensor for the comoving congruence of observers, suggests that no gravitational radiation is produced during the evolution of the system. Instead, the magnetic part of the Weyl tensor as measured by tilted observers is non vanishing (as well as the shear, the four--acceleration, the vorticity and the dissipation), giving rise to a flux of gravitational radiation that can be characterized through the super--Poynting vector. This result strengthens further the relevance of the role of observers in the description of a physical system. An explanation of this dual interpretation in terms of the information theory, is provided.

A benign property of the ghost mode in massive theory of gravitation

It was shown in the frameworks of massive gravitational theories having in linear approximation mass term $${m^2}\left( {{\varphi ^{\alpha \beta }}{\varphi _{\alpha \beta }} - \frac{1}{2}{\varphi ^2}} \right)$$ in the lagrangian, that created some time ago spherically-symmetric static sources should possess inside their light cone not only Yukawa potential, but also nonstationary component. It leads to the long (~ 1/m) period of gravitational evaporation of such sources with the mass loss Ṁ ~ m2M2 The magnitude of the flux is c4/v4 times (с—speed of light, v—velocity of the source particles) bigger then negative gravitational radiation flux corresponding to the ghost scalar mode in the spectrum of such gravitational field, with stabilizing the source.

Relativistic orbits around spinning supermassive black holes: Secular evolution to 4.5 post-Newtonian order

We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the conservative dynamics that are valid through 3PN order, including spin-orbit, quadrupole and (spin)$^2$ effects, and with radiation-reaction contributions linear in the mass of the body that are valid through 4.5PN order, including the 4PN damping effects of spin-orbit coupling. The evolution equations for the osculating orbit elements are iterated to high PN orders using a two-timescale approach and averaging over orbital timescales. We derive a criterion for terminating the orbit when its Carter constant drops below a critical value, whereupon the body plunges across the event horizon at the next closest approach. The results are valid for arbitrary eccentricities and arbitrary inclinations. We then analyze numerically the orbits of objects injected into high-eccentricity orbits via interactions within a surrounding star cluster, obtaining the number of orbits and the elapsed time between injection and plunge, and the residual orbital eccentricity at plunge as a function of inclination. We derive an analytic approximation for the time to plunge in terms of initial orbital variables. We show that, if the black hole is spinning rapidly, the flux of gravitational radiation during the final orbit before plunge may be suppressed by as much as three orders of magnitude if the orbit is retrograde on the equatorial plane compared to its prograde counterpart.

Spectral Cauchy characteristic extraction of strain, news and gravitational radiation flux

We present a new approach for the Cauchy-characteristic extraction (CCE) of gravitational radiation strain, news function, and the flux of the energy–momentum, supermomentum and angular momentum associated with the Bondi–Metzner–Sachs asymptotic symmetries. In CCE, a characteristic evolution code takes numerical data on an inner worldtube supplied by a Cauchy evolution code, and propagates it outwards to obtain the space–time metric in a neighborhood of null infinity. The metric is first determined in a scrambled form in terms of coordinates determined by the Cauchy formalism. In prior treatments, the waveform is first extracted from this metric and then transformed into an asymptotic inertial coordinate system. This procedure provides the physically proper description of the waveform and the radiated energy but it does not generalize to determine the flux of angular momentum or supermomentum. Here we formulate and implement a new approach which transforms the full metric into an asymptotic inertial frame and provides a uniform treatment of all the radiation fluxes associated with the asymptotic symmetries. Computations are performed and calibrated using the spectral Einstein code.

OJ287: Post-Newtonian Calculation in Harmonic Coordinate and Pulsar Timing Residual Confirmation* *Supported by National Natural Science Foundation of China under Grant Nos. 11275187, 11421303, and the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences under Grant No. XDB09000000

We calculate and discuss the motion of the binary black hole OJ287 based on Post-Newtonian approximation in a harmonic coordinate. With gravitational waveform obtained, theoretical timing residual of PSR B1855+09 induced by gravitational radiation of OJ287 is presented and compared with observed data, further shows that hypothesis referring to OJ287 as a binary BH system might be proper. The energy flux of gravitational radiation from binary is also provided, from which we find that the flux changes sign successively: ĖN > 0, Ė1PN < 0, Ė2PN > 0, in agreement with the relative signs of forces of each PN order, revealed in the previous work.

Next-to-leading tail-induced spin–orbit effects in the gravitational radiation flux of compact binaries

The imprint of nonlinearities in the propagation of gravitational waves—the tail effect—is responsible for new spin contributions to the energy flux and orbital phasing of spinning black hole binaries. The spin–orbit (linear in spin) contribution to this effect is currently known at leading post-Newtonian (PN) order, namely 3PN for maximally spinning black holes on quasi-circular orbits. In the present work, we generalize these tail-originated spin–orbit terms to the next-to-leading 4PN order. This requires in particular extending previous results on the dynamical evolution of precessing compact binaries. We show that the tails represent the only spin–orbit terms at that order for quasi-circular orbits, and we find perfect agreement with the known result for a test particle around a Kerr black hole, computed by perturbation theory. The BH-horizon absorption terms have to be added to the PN result computed here. Our work completes the knowledge of the spin–orbit effects to the phasing of compact binaries up to the 4PN order, and will allow the building of more faithful PN templates for the inspiral phase of black hole binaries, improving the capabilities of ground-based and space-based gravitational wave detectors.

Gravitational waves from oscillon preheating

Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks.

Future boundary conditions in de Sitter space

We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.

A proof of Price’s law for the collapse of a self-gravitating scalar field

A well-known open problem in general relativity, dating back to 1972, has been to prove Price's law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux on the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates. It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price's law for the collapse of a self-gravitating scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.'s in 2 independent variables. The technique is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of the first author (gr-qc/0307013) concerning the internal structure of charged black holes, which assumed the validity of Price's law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou's C^0 formulation, the conjecture is proven to be false.

Remarks on theoretical problems in nonsymmetric gravitational theory.

Damour, Deser and McCarthy have claimed that the nonsymmetric gravitational theory (NGT) is untenable due to curvature coupled ghost modes and bad asymptotic behavior. This claim is false for it is based on a physically inaccurate treatment of wave propagation on a curved background and an incorrect method for extracting asymptotic behavior. We show that the flux of gravitational radiation in NGT is finite in magnitude and positive in sign.

Gravitational waves in the nonsymmetric gravitational theory

We prove that the flux of gravitational radiation from an isolated source in the nonsymmetric gravitational theory is identical to that found in Einstein's general theory of relativity.

On the non-radial oscillations of a star - II. Further amplifications

The two algorisms that one uses for determining the complex characteristic frequencies, σ = σ 0 + iσ 1 , belonging to the quasi-normal modes of oscillations of a star, are shown to be equivalent. In the first algorism, one searches directly in the complex σ-plane to satisfy the requirement that at infinity there are only outgoing waves (and no incoming waves). In the second algorism, one restricts oneself to real σs and selects the solution with the minimum flux of gravitational radiation at infinity.

Gravitational radiation field of an isolated system at null infinity

The quadrupole and octupole contributions to the gravitational radiation flux at null infinity from an initially stationary isolated system are computed in terms of the asymptotic moments defined there. The present treatment incorporates the influence of the background field of the source while still neglecting the nonlinear self-interaction of the radiation. Compared with the flat space result, the new formula predicts a suppression of the contribution from the high-frequency modes for which the frequency ω satisfies GM 0 ω / c 3 ≫ 1, M 0 being the initial mass of the system.

Energy loss in general relativity.

Implicit assumptions regarding continuity in energy-loss calculations in general relativity are examined. The Arnowitt-Deser-Misner energy integral is treated in a new manner as a universal vehicle for energy loss. Two explicit examples are given: the electric dipole radiation flux is computed using general relativity as well as the gravitational-radiation flux from a linear mass quadrupole oscillator. In this approach, the latter is seen as a nonlinear problem in the sense that the lower-order metric serves as a source for the required order metric as computed within the wave front. Logarithmic terms which threaten to induce divergences, as has been found in other works, are averted by functions of integration which are required to sustain the gauge conditions and finally yield the usual fluxes.

Direct observational upper limit to gravitational radiation from millisecond pulsar PSR1937 + 214

The newly discovered millisecond pulsar PSR1937 + 214 has such a high rotational rate, 642 Hz, that any significant quadrupole moment not aligned with the spin axis could lead to a large flux of gravitational radiation. Although recently reported slowdown rates suggest an energy loss corresponding to a currently unobservable level of gravitational radiation, existing evidence may not completely rule out all possibilities for production of detectable gravitational waves. For example, continuing accretion might provide additional energy for gravitational radiation; and it may not be impossible that the pulsar might be closer to the Earth than indicated by the dispersion measure if there was large local dispersion. Overall, the parameters of this pulsar seem so exceptional that a direct search for gravitational radiation with existing equipment seemed worth making. We describe here such a search that has set an upper limit to gravitational wave amplitude at twice the pulsar rotation frequency, the observed output from a gravitational wave detector corresponding at this frequency to an amplitude of (0.8^(+1.5) _(−0.8)) × 10^(−20).