The Newman-Penrose Method in the Theory of General Relativity

Frolov, Valeri P.

doi:10.1007/978-1-4684-0676-4_4

Cited by 20 publications

(35 citation statements)

References 109 publications

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“…x is a function of time x ≡ x(t), are denoted as Multiple time derivative from function F (t, x) is denoted by 21) so that its action on the time integrals eliminates integration in the sense that 22) and…”

Section: Notations and Conventionsmentioning

confidence: 99%

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Propagation of light in the field of stationary and radiative gravitational multipoles

Kopeikin

Korobkov

Polnarev

2006

Class. Quantum Grav.

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Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitationalwave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. 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. Present paper suggests physically-adequate and consistent solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system. We derive equations of propagation of electromagnetic wave in the retarded gravitational field of the localized source emitting gravitational waves of arbitrary multipolarity and integrate them analytically in closed form. We also prove that the leading terms in the observable relativistic effects (time delay, deflection angle, and rotation of the plane of polarization of light) depend on the instantaneous value of the multipole moments of the isolated system and its time derivatives taken at the retarded instant of time but not on their integrated values. The influence of the multipolar gravitational field of the isolated system on the light propagation is * To whom correspondence should be addressed (kopeikins@missouri.edu)

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Section: Notations and Conventionsmentioning

confidence: 99%

“…At each point of space-time we introduce a complex null tetrad (l α , n α , m α , m α ) associated with a congruence of light rays [20,21]. It is obvious that such field of complex null tetrads is not uniquely determined by the congruence of null rays and the normalization conditions.…”

Section: Equations For Propagation Of Polarization Propertiesmentioning

confidence: 99%

Propagation of light in the field of stationary and radiative gravitational multipoles

Kopeikin

Korobkov

Polnarev

2006

Class. Quantum Grav.

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“…The eikonal Eq. (3.8) is a direct consequence of Maxwell's equations [3,26,31] and its solution describes a wave front of an electromagnetic wave propagating in curved space-time defined by the metric tensor in Eqs. (2.1), (2.5).…”

Section: The Speed Of Gravity and The Newtonian Limitmentioning

confidence: 99%

“…(3.8) is not related to the specific properties of the electromagnetic field, but is completely determined by the structure of space-time, or, more accurately, its geometry defined by Eqs. (2.1), (2.5) [26].…”

Section: The Speed Of Gravity and The Newtonian Limitmentioning

confidence: 99%

“…Such waves are generated if the second time derivative of the quadrupole moment of the system is not constant [3,25]; that is, the bodies comprising the system accelerate. These gravitational waves, which are type N according to Petrov's classification of gravitational fields [17,26,44], are indeed generated if, and only if, the bodies accelerate. However, the gravitational field of a system emitting gravitational waves also has contributions from other Petrov's type fields -I, II, and III, which have in general relativity the same structure of the null characteristics as the N-type waves, but decay faster with distance from the system so that these near-zone fields can not be observed as freely propagating waves of type N [17].…”

Section: Misconception 4: the Speed Of Gravity Can Only Be Measured Tmentioning

confidence: 99%

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Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment

Kopeikin

Fomalont

2006

Found Phys

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We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7' of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar's radio wave is equivalent to comparison of the relativistic laws of the Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed c, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. In particular, the v/c term beyond of the standard Einstein's deflection, which we measured to 20% accuracy, is associated with the aberration of the null direction of the the gravity force ("aberration of gravity") caused by the Lorentz transformation of the Christoffel symbols from the static frame of Jupiter to the moving frame of observer. General relativistic formulation of the experiment identifies the aberration of gravity with the retardation of gravity because the speed of gravitational waves in Einstein's theory is equal to the speed of propagation of the gravity force. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual-Sánchez, and Carlip and show that their "speed of light" interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar. For this reason, the "speed of light" interpretations are not entirely consistent with a retarded Liénard-Wiechert solution of the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated with the aberration of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c beyond the Shapiro delay, thus, making their measurement highly desirable for deeper testing of general relativity in future astrometric experiments like Gaia, SIM, and SKA.

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