The aim of the present thesis is to review the Blanchet-Damour approach to analytical study of gravitational waves emitted by localized perfect fluid sources. It is assumed these perfect fluids are such that it is possible to define small parameters for asymptotic expansions. Asymptotic expansions in this approach are called post-Minkowskian and post-Newtonian expansions. By plugging these expansions into the Einstein field equation, post-Minkowskian and post-Newtonian equations are obtained. The usual methods for solving these equations are to use the retarded and Poisson integrals. However, they cannot provide solutions up to any arbitrary order in these cases because of their divergence. In fact, these divergences motivated Blanchet and Damour to employ a new approach to solve the post-Minkowskian and post-Newtonian equations. They obtained the general solutions by means of a specific process of analytic continuation. These solutions have some unknown terms that if one determines, the gravitational field is described everywhere in $\mathbb{R}^3$. A matching procedure, which depends deeply on analytic continuation, is used to determine these unknown terms.
We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determinat…
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we compare with numerical results.
We analytically compute the gravitational self-force correction to the gyroscope precession along slightly eccentric equatorial orbits in the Kerr spacetime, generalizing previous results for the Schwarzschild spacetime. Our results are accurate through the 9.5 post-Newtonian order and to second order in both eccentricity and rotation parameter. We also provide a post-Newtonian check of our results based on the currently known Hamiltonian for spinning binaries.
We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part…
Models of gravitational waveforms from coalescing black-hole binaries play a crucial role in the efforts to detect and interpret the signatures of those binaries in the data of large-scale interferometers. Here we summarize recent models that combine information both from analytical approximations and numerical relativity. We briefly lay out and compare the strategies employed to build such complete models and we recapitulate the errors associated with various aspects of the modelling process.
We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in {\it eccentric} orbit around a {\it spinning} black hole. Our results give the redshift contributions that mix eccentricity and spin effects, through second order in eccentricity, second order in spin parameter, and the eight-and-a-half post-Newtonian order.
Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest radius at which a relativistic image might be formed. For horizonless ultracompact objects, additional relativistic images and rings can form inside this radius. In this paper, we provide an analytical approach to deal with strong gravitational lensing from such ultracompact objects, which is substantially different from the black hole cases, first reported …
In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly convergent series and provides extremely accurate approximations already to first order. We have derived a general first order formula for a generic spherically symmetric static metric tensor and we have tested it in four different cases.
This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric Deformation (MGD). For this we apply MGD to Heintzmann's solution obtaining two new analytic and well behaved anisotropic solutions, in which all their parameters such as the effective density, the effective radial and tangential pressure, as well as radial and tangential sound speed, fulfill each of the requirements for the physical acceptability available in …
We develop here a procedure to obtain regular static configurations as resulting from dynamical gravitational collapse of a massive matter cloud in general relativity. Under certain general physical assumptions for the collapsing cloud, we find the class of dynamical models that lead to an equilib- rium configuration. To illustrate this, we provide a class of perfect fluid collapse models that lead to a static constant density object as limit. We suggest that similar models might possibly constitute the basis for the description of formation of compact objects in nature.
We raise the analytical knowledge of the eccentricity-expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the $e^2$ and $e^4$ contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through $e^{20}$. We convert this information into an analytical knowledge of the effective-one-body radial potentials $\bar d(u)$, $ρ(u)$ and $q(u)$ through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force da…
We present a theoretical estimate of the atmospheric Newtonian noise due to fluctuations of atmospheric mass densities generated by acoustic and turbulent phenomena and we determine the relevance of such noise in the laser-interferometric detection of gravitational waves. First, we consider the gravitational coupling of interferometer test-masses to fluctuations of atmospheric density due to the propagation of sound waves in a semispace occupied by an ideal fluid delimited by an infinitely rigid plane. We present an analytical expression of the spectrum of acceleration fluctuations of the test…
The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gauge-invariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian f…
I present an analytical fit to the duration of the inspiral of two point masses driven by gravitational-wave emission. The fit is accurate to within 3% over the entire range of initial eccentricities from 0 to 0.99999.
A class of analytical solutions of axially symmetric vacuum initial data for a self-gravitating system has been found. The active region of the constructed gravitational wave is a thin torus around which the solution is conformally flat. For higher values of gravitational wave amplitude the resulting hypersurface contains apparent horizons.
We develop a non--perturbative method that yields analytical expressions for the deflection angle of light in a general static and spherically symmetric metric. It is an improvement on a method previously devised by the authors, and provides a correct description of the photon sphere already to first order. We also propose an alternative approach that provides general simpler formulas, although with larger errors. We apply our technique to different metrics and verify that the error is at most $0.5 %$ for {\sl all} regimes. We show that our approximation is more accurate than others proposed e…
We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it …
We study the performance of various analytical frequency-domain templates for detection and parameter estimation of gravitational waves from spin-precessing, quasi-circular, compact binary inspirals. We begin by assessing the extent to which non-spinning, spin-aligned, and the new (analytical, frequency-domain, small-spin) double-precessing frequency-domain templates can be used to detect signals from such systems. For effective, dimensionless spin values above $0.2$, the use of non-spinning or spin-aligned templates for detection purposes will result in a loss of up to $30%$ of all events, wh…
We present an alternative derivation of the gravitational clock compass and show how such a device can be used for the detection of gravitational waves. Explicit compass setups are constructed in special types of space--times, namely for exact plane gravitational waves and for waves moving radially relative to an observer.
It is well known that energy fluxes will produce gravitational wave memory. The gravitational wave memory produced by background including cosmic microwave background (CMB), cosmic neutrino background (C$ν$B), and gravitational wave background is investigated in this work. We construct a theory relating the gravitational wave memory strength to the energy flux of a stochastic background. We find that the resulted gravitational wave memory behaves as a constantly varying metric tensor. Such a varying metric tensor will introduce a quadrupole structure to the universe expansion. The gravitationa…
We present an analytical formalism, within the Effective-One-Body framework, which predicts gravitational-wave signals from inspiralling and coalescing black-hole binaries that agree, within numerical errors, with the results of the currently most accurate numerical relativity simulations for several different mass ratios. In the equal-mass case, the gravitational wave energy flux predicted by our formalism agrees, within numerical errors, with the most accurate numerical-relativity energy flux. We think that our formalism opens a realistic possibility of constructing a sufficiently accurate, …
Based on the Szekeres-Pirani gravitational compass we suggest the addition of a fourth, non-coplanar mass/mirror to the presently existing laser based gravitational wave observatories, enabling them to operate omnidirectionally, to filter out ambiguous interpretations and to point out the direction of the gravitational wave source.
In the vicinity of merging neutron strar binaries or supernova remnants, gravitational waves can interact with the prevailing strong magnetic fields. The resulting partial conversion of gravitational waves into electromagnetic (radio) waves might prove to be an indirect way of detecting gravitational waves from such sources. Another interesting interaction considered in this article is the excitation of magnetosonic plasma waves by a gravitational wave passing through the surrounding plasma. The transfer of gravitational wave energy into the plasma might help to fuel the `fireball' of electrom…
We calculate and compare the response of light wave interferometers and matter wave interferometers to gravitational waves. We find that metric matter wave interferometers will not challenge kilometric light wave interferometers such as Virgo or LIGO, but could be a good candidate for the detection of very low frequency gravitational waves.
Gravitational wave science is on the verge of direct observation of the waves predicted by Einstein's General Theory of Relativity and opening the exciting new field of gravitational wave astronomy. In the coming decades, ultra-sensitive arrays of ground-based instruments and complementary spaced-based instruments will observe the gravitational wave sky, inevitably discovering entirely unexpected phenomena while providing new insight into many of the most profound astrophysical phenomena known. in July 2007 the Gravitational Wave International Committee (GWIC) initiated the development of a st…
We discuss image formation in gravitational lensing systems using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from wave functions without using a lens equation for gravitational lensing.
Gravitational wave generation by a strong shock wave in the interaction of high power laser with matter is analyzed in linear approximation of gravitational theory. The analytical formulas and estimates are derived for the metric perturbations and the radiated power of the generated gravitational waves. Furthermore the characteristics of polarization and the behavior of test particles are investigated in the presence of gravitational wave which will be important for the detection.
It is proved that accelerating nondiffracting gravitational Airy wave--packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non--accelerating nondiffracting gravitational wave--packets.
By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.
The physical properties of electromagnetic waves in the presence of a gravitational plane wave are analyzed. Formulas for the Stokes parameters describing the polarization of light are obtained in closed form. The particular case of a constant amplitude gravitational wave is worked out explicitly.
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves. Long wavelength of gravitational waves and compactness of possible sources may enable us to extract information in the interference among the lensed images. We point out that the interference term contains information of relative transverse velocity of the source-lens-observer system, which may be obtained by possible future space-borne gravitational wave dete…
A description is made of the process of excitation of coupled longitudinal-transverse gravitational waves during the propagation of a strong electromagnetic wave in a vacuum and when a standing electromagnetic wave exists in the Fabry-Perot resonator. It is shown that such waves lead to the appearance of transverse gravitational waves in empty space. It was established that two standing high-frequency electromagnetic waves in a Fabry-Perot resonator with close frequencies cause the appearance of a low-frequency transverse gravitational wave in empty space.
The dynamics of a gravitational wave propagating through a cosmic gauge field are dramatically different than in vacuum. We show that a gravitational wave acquires an effective mass, is birefringent, and its normal modes are a linear combination of gravitational waves and gauge field excitations, leading to the phenomenon of gravitational wave -- gauge field oscillations. These surprising results provide insight into gravitational phenomena and may suggest new approaches to a theory of quantum gravity.
A theoretical description of electromagnetic waves in the background of a (weak) gravitational wave is presented. Explicit expressions are obtained for the Stokes parameters during the passage of a plane-fronted gravitational wave described by the Ehlers-Kundt metric. In particular, it is shown that the axis of the polarization ellipse oscillates, its ellipticity remaining constant.
We consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational and scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational wave. Some reflection processes are given for different choice of packets in which the Coulomb-like component $Ψ_2$ vanishes. Exact solution for multiple reflection of an electromagnetic wave from successive impulsive gravitational waves is obtained in a closed form. It is shown that a succesive sign flip in the Maxwell spinor arises as a result of encountering with an impulsive trai…
A different approach has been used to evaluate the momentum imparted by the gravitational waves with spherical wavefronts. It is shown that the results obtained for momentum coincide with those already available in the literature.
Spinorial formalism is used to map every electromagnetic wave into the gravitational wave (within the linearized gravity). In this way we can obtain the gravitational counterparts of Bessel, Laguerre-Gauss, and other light beams carrying orbital angular momentum.
We calculate momentum imparted by colliding gravitational waves in a closed Friedmann Robertson-Walker background and also by gravitational waves with toroidal wavefronts using an operational procedure. The results obtained for toroidal wavefronts are well behaved and reduce to the spherical wavefronts for a special choice.
We investigate the hypothetical process of gravitational Cherenkov radiation, which may occur in modified gravity theories. We obtain a useful constraint on a modified dispersion relation for propagating modes of gravitational waves, which could be predicted as a consequence of violation of the Lorentz invariance in modified theories of gravity. The constraint from gravitational Cherenkov radiation and that from direct measurements of the gravitational waves emitted by a compact binary system are complementary to each other.
In conventional gravitational wave scattering theory, a large-distance asymptotic approximation is employed. In this approximation, the gravitational wave is approximated by its large-distance asymptotics. In this paper, we establish a gravitational wave scattering theory without the large-distance asymptotic approximation.
The polarization of electromagnetic waves in the presence of a gravitational wave is analyzed. The rotation of the polarization angle and the Stokes parameters are deduced. A possible application to the detection of stochastic background of gravitational waves is proposed as a complement to the pulsar timing method.
We discuss a gravitationally induced nonlinearity in hierarchic systems. We consider the generation of extremely low-frequency radio waves with a frequency of the periodic gravitational radiation; the generation is due to an induced nonlinear self-action of electromagnetic radiation in the vicinity of the gravitational-radiation source. These radio waves are a fundamentally new type of response of an electrodynamic system to gravitational radiation. That is why we here use an unconventional term: radio-wave messengers of periodic gravitational radiation.
We examine a simple model of interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of gravitational wave when passing through media. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.
Gravitational wave memory is an important prediction of general relativity. The detection of the gravitational wave memory can be used to test general relativity and to deduce the property of the gravitational wave source. Quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory always use the energy flux of gravitational wave to calculate memory. Such relation between gravitational wave energy and memory has only been validated for post-Newtonian approximation. The result of numerical relativity about gravitational wave memory i…
Two different approaches to gravitational perturbation theory appear to give two different answers for the properties of gravitational wave memory. We show that this contradiction is only apparent and the two approaches actually agree.
The first generation of gravitational wave interferometric detectors has taken data at, or close to, their design sensitivity. This data has been searched for a broad range of gravitational wave signatures. An overview of gravitational wave search methods and results are presented. Searches for gravitational waves from unmodelled burst sources, compact binary coalescences, continuous wave sources and stochastic backgrounds are discussed.
We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to construct a piecewise flat spacetime that describes an impulsive plane wavefront. From these wavefronts more general plane waves may be constructed.
We consider the propagation of strong gravitational waves interacting with a nonperturbative vacuum of spinor fields. To described the latter, we suggest an approximate model. The corresponding Einstein equation has the form of the Schrödinger equation. Its gravitational-wave solution is analogous to the solution of the Schrödinger equation for an electron moving in a periodic potential. The general solution for the periodic gravitational waves is found. The analog of the Kronig-Penney model for gravitational waves is considered. It is shown that the suggested gravitational-wave model permits …
A class of solutions of the gravitational field equations describing vacuum spacetimes outside rotating cylindrical sources is presented. A subclass of these solutions corresponds to the exterior gravitational fields of rotating cylindrical systems that emit gravitational radiation. The properties of these rotating gravitational wave spacetimes are investigated. In particular, we discuss the energy density of these waves using the gravitational stress-energy tensor.
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of gravitational waves via a spin-orbit coupling mechanism. We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. The effecti…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations and work out the corresponding gravitational wave equation. Moreover we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating $n$-body systems and present some aspects of the current interfe…
We analyze the gravitational waves within the Spinor Theory of Gravity and compare it with the General Relativity proposal. In the case of STG a gravitational wave may occur if the effective gravitational metric induced by the spinorial field is Ricci flat.
