Gravitational Radiation Theory and Light Propagation

The paper gives an introduction to the gravitational radiation theory of isolated sources and to the propagation properties of light rays in radiative gravitational fields. It presents a theoretical study of the generation, propagation, back-reaction, and detection of gravitational waves from astrophysical sources. After reviewing the various quadrupole-moment laws for gravitational radiation in the Newtonian approximation, we show how to incorporate post-Newtonian corrections into the source multipole moments, the radiative multipole moments at infinity, and the back-reaction potentials. We further treat the light propagation in the linearized gravitational field outside a gravitational wave emitting source. The effects of time delay, bending of light, and moving source frequency shift are presented in terms of the gravitational lens potential. Time delay results are applied in the description of the procedure of the detection of gravitational waves

Gravitomagnetic Effects in the Propagation of Electromagnetic Waves in Variable Gravitational Fields of Arbitrary-Moving and Spinning Bodies

Propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed. The gravitational field is assumed to be "weak" everywhere. Equations of motion of a light ray are solved in the first post-Minkowskian approximation that is linear with respect to the universal gravitational constant $G$. We do not restrict ourselves with the approximation of gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of source of light and observer. This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of pulsar and its companion. We also derive the correction to the light deflection angle caused by rotation of gravitating bodies in the solar system (Sun, planets) or a gravitational lens. The gravitational shift of frequency due to the combined translational and rotational motions of light-ray-deflecting bodies is analyzed as well. We give a general derivation of the formula describing the relativistic rotation of the plane of polarization of electromagnetic waves (Skrotskii effect). This formula is valid for arbitrary translational and rotational motion of gravitating bodies and greatly extends the results of previous researchers. Finally, we discuss the Skrotskii effect for gravitational waves emitted by localized sources such as a binary system. The theoretical results of this paper can be applied for studying various relativistic effects in microarcsecond space astrometry and developing corresponding algorithms for data processing in space astrometric missions such as FAME, SIM, and GAIA.Comment: 36 pages, 1 figure, submitted to Phys. Rev.

General Relativistic Theory of Light Propagation in the Field of Radiative Gravitational Multipoles

The extremely high precision of current radio/optical interferometric observations and the unparalleled sensitivity of existing (LIGO) and future (LISA, ASTROD) gravitational-wave detectors demand a much better theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. A consistent approach giving a complete and exhaustive solution to this problem in the first post-Minkowskian approximation of General Relativity is presented in this paper. We derive a set of equations describing propagation of an electromagnetic wave in the retarded gravitational field of a time-dependent localized source emitting gravitational waves with arbitrary multipolarity and show for the first time that they can be integrated analytically in closed form. We also prove that the leading terms in observable relativistic effects depend exclusively on the values of the multipole moments of the isolated system and its time derivatives taken at the retarded instant of time on the null cone and do not depend on their integrated values. By making use of our integration technique we reproduce the known results of integration of equations of light rays both in a stationary field of a gravitational lens and in that of a plane gravitational wave, thereby establishing a relationship between our formalism and the approximations used by previous researches. The gauge freedom of our formalism is carefully studied and all gauge-dependent terms in the expressions for observable quantities are singled out and used for physically meaningful interpretation of observations. Two limiting cases of small and large values of the light-ray impact parameter, d, are elaborated in more detail. We explicitly show that in the case of small impact parameter the leading order terms for any effect of light propagation in the field of an arbitrary multipole depend neither on its radiative nor on its intermediate zone contributions. The main effect rather comes from the near zone terms. This property makes much more difficult any direct detection of gravitational waves by astronomical techniques if general relativity is correct. We also present an analytical treatment of time delay and light-ray bending in large impact parameter case corresponding to the approximation of a plane gravitational wave of arbitrary multipolarity. Explicit expressions for time delay and deflection angle are obtained in terms of the transverse-traceless (TT) part of the space-space components of the metric tensor