Theory Of Gravitational Waves Research Articles

On the transverse-traceless gauge condition when matter is presented

The transverse-traceless gauge condition is an important concept in the theory of gravitational waves. It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge. Although it is thin, the interstellar medium is ubiquitous in the Universe. Therefore, it is important to understand the concept of gravitational waves when matter is presented. Bondi–Metzner–Sachs theory has solved the gauge problem related to gravitational waves. But it does not help with cases when the gravitational wave propagates in matter. This paper discusses possible extensions of the transverse-traceless gauge condition to Minkowski perturbation with matter presented.

On the viscoelastic-electromagnetic-gravitational analogy

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.

Biorthogonal harmonics for the decomposition of gravitational radiation. I. Angular modes, completeness, and the introduction of adjoint-spheroidal harmonics

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications in signal modeling and data analysis. This problem is complicated by most astrophysically relevant systems not having modes that are analytically tractable. A ubiquitous workaround is to use not modes, but multipole moments defined by spin-weighted spherical harmonics. However, spherical multipole moments are only related to the modes of systems without angular momentum. As a result, they can obscure the underlying physics of astrophysically relevant systems, such as binary black hole merger and ringdown. In such cases, spacetime angular momentum means that radiative modes are not spherical, but spheroidal in nature. Here, we work through various problems related to spheroidal harmonics. We show for the first time that spheroidal harmonics are not only capable of representing arbitrary gravitational wave signals, but that they also possess a kind of orthogonality not used before in general relativity theory. Along the way we present a new class of spin-weighted harmonic functions dubbed ``adjoint-spheroidal'' harmonics. These new functions may be used for the general estimation of spheroidal multipole moments via complete biorthogonal decomposition (in the angular domain). By construction, adjoint-spheroidal harmonics suppress mode-mixing effects known to plague spherical harmonic decomposition; as a result, they better approximate a system's true radiative modes. We discuss potential applications of these results. Lastly, we briefly comment on the challenges posed by the analogous problem with Teukolsky's radial functions.

Curvature Dynamics in General Relativity

The equations of general relativity are recast in the form of a wave equation for the Weyl tensor. This allows reformulation of gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse polarization states for curvature waves is proven and in the linearized approximation the quadrupole formula is rederived. A perturbative scheme to extend the linearized result to the non-linear regime is outlined.

Analytical coordinate time at first post-Newtonian order

In this letter, we exploit the Damour-Deruelle solution to derive the analytical expression of the coordinate time in terms of the polar angle. This formula has advantageous applications in both pulsar timing and gravitational-wave theory.

Gravitational Waves from Generalized Newtonian Sources

AbstractI review the elementary theory of gravitational waves on a Minkowski background and the quadrupole approximation. The modified conservation laws for energy and momentum keeping track of the gravitational‐wave flux are presented. The theory is applied to two‐body systems in bound and scattering states subject to newtonian gravity generalized to include a force allowing for orbital precession. The evolution of the orbits is studied in the adiabatic approximation. From these results I derive the conditions for capture of two bodies to form a bound state by the emission of gravitational radiation.

Quadrupolar power radiation by a binary system in de Sitter background

Cosmological observations over past couple of decades favor our universe with a tiny positive cosmological constant. Presence of cosmological constant not only imposes theoretical challenges in gravitational wave physics, it has also observational relevance. Inclusion of cosmological constant in linearized theory of gravitational waves modifies the power radiated quadrupole formula. There are two types of observations which can be impacted by the modified quadrupole formula. One is the orbital decay of an inspiraling binary and other is the modification of the waveform at the detector. Modeling a compact binary system in an elliptic orbit on de Sitter background, we obtain energy and angular momentum radiation due to emission of gravitational waves. We also investigate the evolution of orbital parameters under back reaction and its impact on orbital decay rate. In the limit to circular orbit, our result matches to that obtained in [B. Bonga and J. S. Hazboun, Phys. Rev. D 96 (2017) 064018, arXiv:1708.05621 ].

并合双星系统的“共旋”引力波理论模型

并合双星系统的“共旋”引力波理论模型

Field theoretical approach to gravitational waves

The aim of these notes is to give an accessible and self‐contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincaré group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system.

Obtaining gravitational waves from inspiral binary systems using LIGO data

The discovery of the astrophysical events GW150926 and GW151226 has experimentally confirmed the existence of gravitational waves (GW) and has demonstrated the existence of binary stellar-mass black hole systems. This finding marks the beginning of a new era that will reveal unexpected features of our universe. This work presents a basic insight to the fundamental theory of GW emitted by inspiral binary systems and describes the scientific and technological efforts developed to measure these waves using the interferometer-based detector called LIGO. Subsequently, the work presents a comprehensive data analysis methodology based on the matched filter algorithm, which aims to recovery GW signals emitted by inspiral binary systems of astrophysical sources. This algorithm was evaluated with freely available LIGO data containing injected GW waveforms. Results of the experiments performed to assess detection accuracy showed the recovery of 85% of the injected GW.

Modal series expansions for plane gravitational waves

Propagation of gravitational disturbances at the speed of light is one of the key predictions of the General Theory of Relativity. This result is now backed indirectly by the observations of the behaviour of the ephemeris of binary pulsar systems. These new results have in- creased the interest in the mathematical theory of gravitational waves in the last decades and several mathematical approaches have been developed for a better understanding of the solutions. In this paper we develop a modal series expansion technique in which solutions can be built for plane waves from a seed integrable function. The convergence of these series is proven by the Raabe- Duhamel criteria and we show that these solutions are characterized by a well-defined and finite curvature tensor and also a finite energy content.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant.

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ, however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ>0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Gravitational wave astronomy: the current status

In the centenary year of Einstein's General Theory of Relativity, this paper reviews the current status of gravitational wave astronomy across a spectrum which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper reviews the historical development of gravitational wave astronomy from Einstein's first prediction to our current understanding the spectrum. It is shown that detection of signals in the audio frequency spectrum can be expected very soon, and that a north-south pair of next generation detectors would provide large scientific benefits. Sect. 2 reviews the theory of gravitational waves and the principles of detection using laser interferometry. The state of the art Advanced LIGO detectors are then described. These detectors have a high chance of detecting the first events in the near future. Sect. 3 reviews the KAGRA detector currently under development in Japan, which will be the first laser interferometer detector to use cryogenic test masses. Sect. 4 of this paper reviews gravitational wave detection in the nanohertz frequency band using the technique of pulsar timing. Sect. 5 reviews the status of gravitational wave detection in the attohertz frequency band, detectable in the polarisation of the cosmic microwave background, and discusses the prospects for detection of primordial waves from the big bang. The techniques described in sects. 1-5 have already placed significant limits on the strength of gravitational wave sources. Sects. 6 and 7 review ambitious plans for future space based gravitational wave detectors in the millihertz frequency band. Sect. 6 presents a roadmap for development of space based gravitational wave detectors by China while sect. 7 discusses a key enabling technology for space interferometry known as time delay interferometry.

Maxwellian theory of gravitational waves and their mechanical properties

We present a theory in Maxwellian form for gravitational waves in a flat background. This requires us to identify the gravitational analogues of the electric and magnetic fields for light. An important novelty, however, is that our analogues are not vector fields but rather rank-two tensor fields; in place of a three-component vector at each point in space, as in electromagnetism, our fields are three by three symmetric matrices at each point. The resulting Maxwell-like equations lead directly to a Poynting theorem for the local energy density associated with a gravitational wave and to associated local properties including densities of momentum and angular momentum.

A DETAILED PROOF OF THE FUNDAMENTAL THEOREM OF STF MULTIPOLE EXPANSION IN LINEARIZED GRAVITY

The linearized field equations of general relativity in harmonic coordinates are given by an inhomogeneous wave equation. In the region exterior to the matter field, the retarded solution of this wave equation can be expanded in terms of 10 Cartesian symmetric and tracefree (STF) multipoles in post-Minkowskian approximation. For such a multipole decomposition only three and rather weak assumptions are required: (1) No-incoming-radiation condition. (2) The matter source is spatially compact. (3) A spherical expansion for the metric outside the matter source is possible. During the last decades, the STF multipole expansion has been established as a powerful tool in several fields of gravitational physics: celestial mechanics, theory of gravitational waves and in the theory of light propagation and astrometry. But despite its formidable importance, an explicit proof of the fundamental theorem of STF multipole expansion has not been presented so far, while only some parts of it are distributed into several publications. In a technical but more didactical form, an explicit and detailed mathematical proof of each individual step of this important theorem of STF multipole expansion is represented.

Application of the Non-Local Physics in the Theory of Gravitational Waves and Big Bang

The theory of gravitational waves in the frame of non-local quantum hydrodynamics (NLQH) is considered. From calculations follow that NLQH equations for “empty” space have the traveling wave solutions belonging in particular to the soliton class. The possible influence and reaction of the background microwave radiation is taken into account. These results lead to the principal correction of the inflation theory and serve as the explanation for the recent discovery of the universe’s cosmic microwave background anomalies. The simple analytical particular cases and numerical calculations are delivered. Proposal for astronomers—to find in the center domain of the hefty cold spot the smallest hot spot as the origin of the initial burst—Big Bang.

중력파와 천문학

Gravitational waves are predicted by the Einstein's theory of General Relativity. The direct detection of gravitational waves is one of the most challenging tasks in modern science and engineering due to the 'weak' nature of gravity. Recent development of the laser interferometer technology, however, makes it possible to build a detector on Earth that is sensitive up to 100-1000 Mpc for strong sources. It implies an expected detection rate of neutron star mergers, which are one of the most important targets for ground-based detectors, ranges between a few to a few hundred per year. Therefore, we expect that the gravitational-wave observation will be routine within several years. Strongest gravitational-wave sources include tight binaries composed of compact objects, supernova explosions, gamma-ray bursts, mergers of supermassive black holes, etc. Together with the electromagnetic waves, the gravitational wave observation will allow us to explore the most exotic nature of astrophysical objects as well as the very early evolution of the universe. This review provides a comprehensive overview of the theory of gravitational waves, principles of detections, gravitational-wave detectors, astrophysical sources of gravitational waves, and future prospects.

GRAVITATIONAL WAVES FROM COALESCING BINARY SOURCES

Coalescing binary systems (e.g. pulsars, neutron stars and black holes) are currently considered to be the most likely sources of gravitational radiation, yet to be detected on or near Earth, where the local gravitational field is negligible and the Poincaré symmetry rules. On the other hand, the general theory of gravitational waves emitted by axially symmetric rotating sources predicts the existence of a nonvanishing news function. The existence of such function implies that, for a distant observer, the asymptotic group of isometries, the BMS group, has a translational symmetry that depends on the orbit periodicity of the source, thus breaking the isotropy of the Poincaré translations. These results suggest that the asymptotic BMS-covariant wave equation should be applied to obtain a proper theoretical basis for the gravitational waves observations from those binary sources.

Solution of Maxwell’s equations on a de Sitter background

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space–time studied in static spherical coordinates. There is no source besides the background. One component of the vector field is expressed, in its radial part, through the solution of a fourth-order ordinary differential equation obeying given initial conditions. The other components of the vector field are then found by acting with lower-order differential operators on the solution of the fourth-order equation (while the transverse part is decoupled and solved exactly from the beginning). The whole four-vector potential is eventually expressed through hypergeometric functions and spherical harmonics. Its radial part is plotted for given choices of initial conditions. We have thus completely succeeded in solving the homogeneous vector wave equation for Maxwell theory in the Lorenz gauge when a de Sitter space–time is considered, which is relevant both for inflationary cosmology and gravitational wave theory. The decoupling technique and analytic formulae and plots are completely original. This is an important step towards solving exactly the tensor wave equation in de Sitter space–time, which has important applications to the theory of gravitational waves about curved backgrounds.

Evolution of cosmological gravitational waves inf(R)gravity

We give a rigorous and mathematically clear presentation of the covariant and gauge-invariant theory of gravitational waves in a perturbed Friedmann-Lema\^{\i}tre-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of tensor perturbations in fourth order gravity, we apply the formalism to a simple background solution of ${R}^{n}$ gravity. We obtain the exact solutions of the perturbation equations for scales much bigger than and smaller than the Hubble radius. It is shown that the evolution of tensor modes is highly sensitive to the choice of $n$ and an interesting new feature arises. During the radiation dominated era, their exists a growing tensor perturbation for nearly all choices of $n$. This occurs even when the background model is undergoing accelerated expansion as opposed to the case of general relativity. Consequently, cosmological gravitational wave modes can in principle provide a strong constraint on the theory of gravity independent of other cosmological data sets.