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The theoretical foundations of metric theories of gravitation rest largely on the Einstein equivalence principle (EEP). Schiff has conjectured that no consistent Lorentz-invariant theory can obey the weak equivalence principle and not obey the EEP. However, a counterexample has been proposed by Ni in a theoretical framework for studying electromagnetism coupled to gravity. Under the assumption that gravitational fields vary smoothly over a Hubble time, we show that Ni's counterexample would lead to a rotation in the plane of polarization of radiation from distant ratio sources

The equivalence principle of general relativity asserts that, locally, gravitation is completely indistinguishable from the inertial “pseudo‐force” one would experience in an appropriately contrived accelerated frame. This implies the precise equality of gravitational and inertial mass, irrespective of a body's makeup. And, from special relativity, we know that a body's inertial mass is given by its total energy in its rest frame.

Some years ago, a new powerful technique, known as the Classical Effective Field Theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically important issues, such as gravitational radiation in any spacetime dimension. In particular, we derive for the first time the Einstein-Infeld-Hoffman Lagrangian and we compute Einstein's quadrupole formula for any number of flat spacetime dimensions., Comment: 32 pages, 10 figures. v2: Factor in eq. (3.11) fixed. References added

The Green-Schwarz anomaly-cancelling mechanism in string theories requires a Chern-Simons term in the Einstein-Hilbert action, which leads to an amplitude birefringence of spacetime for the propagation of gravitational waves. While the degree of birefringence may be intrinsically small, its effects on a gravitational wave will accumulate as the wave propagates. The proposed Laser Interferometer Space Antenna (LISA) will be sensitive enough to observe the gravitational waves from sources at cosmological distances great enough that interesting bounds on the Chern-Simons may be found. Here we evaluate the effect of a Chern-Simons induced spacetime birefringence to the propagation of gravitational waves from such systems. We find that gravitational waves from in coalescing binary black hole system are imprinted with a signature of Chern-Simons gravity. This signature appears as a time-dependent change in the apparent orientation of the binary's orbital angular momentum with respect to the observer line-of-sight, with the change magnitude reflecting the integrated history of the Chern-Simons coupling over the worldline of a radiation wavefront. While spin-orbit coupling in the binary system will also lead to an evolution of the system's orbital angular momentum, the time dependence and other details of this \emph{real} effect are different than the \emph{apparent} effect produced by Chern-Simons birefringence, allowing the two effects to be separately identified., Comment: 14 pages, no figures, submitted to Phys. Rev. D

The fact that gravity is a metric theory follows from the Einstein equivalence principle. This principle consists of (i) the universality of free fall, (ii) the universality of the gravitational redshift and (iii) the local validity of Lorentz invariance. Many experiments searching for deviations from standard general relativity test the various aspects of the Einstein equivalence principle. Here we report on experiments covering the whole Einstein equivalence principle. Until now all experiments have been in agreement with the Einstein equivalence principle. As a consequence, gravity has to be described by a metric theory. Any metric theory of gravity leads to effects such as perihelion shift, deflection of light, gravitational redshift, gravitational time delay, Lense?Thirring effect, Schiff effect, etc. A particular theory of that sort is Einstein's general relativity. For weak gravitational fields which are asymptotically flat any deviation from Einstein's general relativity can be parametrized by a few constants, the PPN parameters. Many astrophysical observations and space experiments are devoted to a better measurement of the effects and, thus, of the PPN parameters. It is clear that gravity is best tested for intermediate ranges, that is, for distances between 1 m and several astronomical units. It is highly interesting to push forward our domain of experience and to strengthen the experimental foundation of gravity also beyond these scales. This point is underlined by the fact that many quantum gravity and unification-inspired theories suggest deviation from the standard laws of gravity at very small or very large scales. In this session summary we briefly outline the status and report on the talks presented in session C1 about experimental gravitation.

This paper was published online on 10 January 2008 with a formatting error in the forty-ninth affiliation in the author list. The affiliation should read as ‘‘University of Western Australia, Crawley, WA 6009, Australia.’’ The affiliation hasbeen corrected as of 29 February 2008. The affiliation is incorrect in the printed version of the journal.

This paper was published online on 29 October 2007 with a formatting error in the fiftieth affiliation in the author list. The affiliation should read as ‘‘University of Western Australia, Crawley, WA 6009, Australia.’’ The affiliation has been corrected as of 4 March 2008. The affiliation is incorrect in the printed version of the journal.

After a brief review of the work of de Paula, Miranda and Marinho on massive gravitational waves arising from a bimetric theory of gravity, in this paper it is shown that the presence of the mass generates a longi- tudinal component in a particular polarization of the wave. The effect of this polarization on test masses is performed using the geodesic deviation. A the end of this paper the detectability of this particular polarization is also discussed, showing that its angular dependence could, in princi- ple, discriminate such polarization with respect the two ones of general relativity, if present or future detectors will achieve a high sensitivity., Comment: Published in Astroparticle Physics

Tests of the gravitational redshift effect provide a way to check the validity of the Einstein Equivalence Principle (EEP) and, more specifically, of general relativity. If the EEP is valid, then the redshift should be the same for different clocks. Also, according to general relativity, the redshift should depend upon only the total mass of a gravitating body without reference to its detailed composition. These predictions have been tested mainly in the gravitational field of the Earth. It is now possible to measure, with space probes, the redshift effect to good accuracy in the vicinity of other bodies in the solar system, in particular at the massive outer planets. The present and future status of these experiments is discussed.

A study of kinematics of a 2-body system is used to show that the Mach principle, previously rejected by general relativity, can still serve as an alternative to the concept of absolute space, if one assumes that the background of distant stars determines both the inertial and the gravitational masses of a body.

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.

In this paper we bring to light an hitherto undisclosed richness of this Theory, namely its admitting a consistent reformulation which is able to provide a unified scenario for all kinds of particles, be they lightlike or not. This result hinges on a "generalized" Principle of Relativity which is {intrinsic} to Einstein's Theory. The road leading to this generalization starts, in the very spirit of Relativity, from enhancing full equivalence between the four spacetime directions by requiring full equivalence between the "motions" along these four spacetime directions as well. So far, no measurable spatial velocity in the direction of the time axis has ever been defined, on the same footing of the usual velocities in the local three-space of a given observer. In this paper, we show how Relativity allows such a "time-velocity" to be defined in a very natural way, for any particle and in any reference frame. As a consequence of this natural definition, it also follows that the time- and space-velocity vectors sum up to define a spacelike "world-velocity" vector, the modulus of which turns out to be equal to the Maxwell's constant c, irrespective of the observer who measures it. This {measurable} world-velocity therefore represents the speed at which "all" kinds of particles move in spacetime, according to any observer. As remarked above, the unifying scenario thus emerging is intrinsic to Einstein's Theory; it extends the role traditionally assigned to Maxwell's constant c, and can therefore justly be referred to as "a generalized Principle of Relativity"., 18 pages, no figures

There are conflicting statements in the literature about the gravitational Faraday rotation of the plane of polarization of polarized electromagnetic radiation travelling through a gravitational wave. This issue is reconsidered using a simple formalism describing the rotation of the plane of polarization in a gravitational field, in the geometric optics approximation. It is shown that, to first order in the gravitational wave amplitude, the rotation angle is a boundary effect which vanishes for localized (astrophysically generated) gravitational waves and is non-zero, but nevertheless negligible, for cosmological gravitational waves., 11 pages, latex, to appear in New Astronomy

If the gravitational metric tensor field of Einstein’s General Relativity is supplemented by other long range, very weakly coupled interaction fields, then General Relativity’s Equivalence Principle foundations are violated, or its post-Newtonian (1/c 2order) structure is altered, or both. Space experiments test for and measure such possibilities; presently universality of free fall is confirmed to about a part in 1012, and no deviations of post-Newtonian metric gravity from general relativity are seen down to the few parts in 104 level. Future experiments in space can significantly increase the precision to which fundamental physical law is probed. In particular, transponded interplanetary laser ranging can measure presence of metrically coupled scalar fields in gravity with two or three orders of magnitude higher precision than past experiments, and can begin to measure the second post-Newtonian (1/c 4) structure of gravity. A space-based experiment of the universality of free-fall (STEP) can detect additional interactions of a non-metric nature with five or six orders of magnitude higher precision than today’s experiments.

We study some effects when a probe light pulse propagates in the spacetime curved by the gravitational field of high-power laser pulses. The gravitational field produced by a high-power laser is calculated by using the linearized Einstein field equation under the weak field approximation. It is found that the gravitational modification of the photon Berry phase occurs when the probe light pulse transports in a uniform winding fiber in this gravitational background. We also find the gravitational redshifting and defocusing for the probe pulse caused by the gravitational field of the high-power lasers.

1. Gravity has long eluded theoretical investigation, and, apart from the meager knowledge gained by experience, the main reason is that the gravitational field exhibits the peculiarity that the field itself is amplified when it performs external work. It is therefore difficult to design the theory so that it does not conflict with the energy principle. Admittedly the magnetic field of two current-carrying conductors shows the same peculiarity. However, in that case one readily recognizes in the apparatus that provides the current the source of energy both for the energy increase of the magnetic field and for the energy carried off as work. For the gravitational field such an external energy source is absent, and therefore one formerly used to assume in gravitational theories that the energy of the field is negative, so that upon amplification of the field a positive energy is released and is manifested as work gained. Every theory of gravitation that is built upon the scheme of Maxwell ’ s equations must make the assumption of a negative energy. But this assumption is untenable, because a field whose energy is negative cannot be in stable equilibrium, but is always unstable. Namely, whereas an electrostatic field, for example, exhibits that distribution of lines of force for which the energy has the smallest possible value, a field that is similarly constituted but with negative energy has of course precisely the largest possible value at equilibrium. It is therefore to be expected that when the equilibrium is slightly perturbed, the field will continually release energy to the exterior | while simultaneously moving further and further away from its equilibrium state. So in this way one does not attain a satisfactory theory of gravity. A simple, feasible way leading out of this difficulty was first indicated by M. Abraham. 1 This way consists of including in the state variables, upon which the

General Relativity today.- Beyond Einstein's Gravity.- The Double Pulsar.- Testing Einstein in Space: The Gravity Probe B Relativity Mission.- Instruments for Gravitational Wave Astronomy on Ground and in Space.

The gravitational wave detector VIRGO is in the final commissioning phase and some preliminary data has already been acquired. The aim of VIRGO is to directly detect gravitational waves emitted by compact objects at the time of coalescence and by other astrophysical sources. Here we report on the present sensitivity for detecting these sources and what we will achieve in the near future. We also discuss some details of our data analysis methods and we show some preliminary results related to the fraction of the Universe that we can observe.

This paper begins by reviewing the development of gravitational wave astronomy from the first predictions of gravitational waves to development of technologies across the entire gravitational wave spectrum, and then focuses on the current status of ground based gravitational wave detectors. With substantial improvements already demonstrated in early commissioning it is emphasised that Advanced detectors are on track for first detection of gravitational waves. The importance of a worldwide array of detectors is emphasised, and recent results are shown that demonstrate the continued advantage of a southern hemisphere detector. Finally it is shown that a north–south pair of 8 km arm length detectors would give rise to a dramatic improvement in event rate, enabling a pair of detectors to encompass a 64-times larger volume of the universe, to conduct a census on all stellar mass black hole mergers to [Formula: see text] and to observe neutron star mergers to a distance of [Formula: see text][Formula: see text]800 Mpc.

In this paper, we discuss the essential element of gravity as spacetime curvature and a gravitational wave as the propagation of spacetime curvature. Electromagnetic waves are necessarily localized carriers of spacetime curvature and hence are also gravitational waves. Thus, electromagnetic waves have dual character and detection of gravitational waves is the routine of our everyday experience. Regarding the transferring energy from a gravitational wave to an apparatus, both Rosen and Bondi waves lack the essential characteristic of inducing a gradient of acceleration between detector elements. We discuss our simple invariant energy expression for general relativity and its extension. If the cosmological term is present in the field equations, its universal presence characteristic implies that gravitational waves would necessarily have an energy aspect in their propagation in every case.

The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 1042G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature A. This paper gives an overview of the authors' works [1, 2, 3, 4], which set out the relevant results. Additionally, data is provided on the broadening of the spectra characteristic radiation. The data show that this broadening can be explained only by the presence of excited states of electrons in their gravitational field. What is more, the interpretation of the new line of X-ray emission spectrum according to the results of observation of MOS-camera of XMM-Newton observatory is of interest. The given work contributes into further elaboration of the findings considering their application to dense high- temperature plasma of multiple-charge ions. This is due to quantitative character of electron gravitational radiation spectrum such that amplification of gravitational radiation may take place only in multiple-charge ion high-temperature plasma.

As currently conceived, the proposed MiniSTEP experiment is designed to test, with an accuracy of 1 part in 10 18 , the equivalence of inertial and gravitational mass. Within the experimental payload concentric pairs of test masses, made from different materials, will be in ‘free fall’ as they orbit around the Earth inside a drag-free spacecraft. Any violation of the Equivalence Principle will be disclosed during the experiment by the existence of a differential acceleration between the masses comprising each pair, as detected by SQUID-based sensors. Four pairs of masses are to be used, each pair forming a differential accelerometer. The experiment will employ existing space technology and cryogenic techniques in order to reach this unprecedented level of accuracy.

Expression for second post-Newtonian level gravitational deflection angle of massive particles is obtained in a model independent framework. Several of its important implications including the possibility of testing gravitational theories at that level are discussed., 5 pages, couple of equations of the previous version are corrected

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries., Comment: 35 pages

We review the current status of experimental tests of general relativity, and describe future experiments in the LISA time frame that may improve the empirical underpinning of the theory.

We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.

In special relativity the chronogeometrical structure is absolute and there is no notion of instantaneous 3‐space: distant clock synchronization is based on a convention, which changes going from inertial to non‐inertial frames. On the contrary in Einstein general relativity the metric tensor has a double role: 1) it is the mediator of the gravitational interaction; 2) it determines the dynamical chronogeometrical structure of spacetime. As a consequence, it “teaches relativistic causality” to to every other field with the following implications: a) the conventions for distant clock synchronization in non‐inertial frames are dynamically determined; b) the 8 arbitrary gauge variables hidden in the metric tensor describe “inertial effects” in non‐inertial frames; c) the Dirac observables of the gravitational field describe “tidal effects” in non‐inertial frames. A Hamiltonian reading of Bergmann‐Komar intrinsic pseudo‐coordinates, in connection with Einstein’s Hole Argument, leads to a identification of the notions of “spacetime” and “gravitational field”, which must be taken into account in any approach to quantum gravity.

We show that if the visible universe is a membrane embedded in a higher-dimensional space, particles in uniform motion radiate gravitational waves because of spacetime lumpiness. This phenomenon is analogous to the electromagnetic diffraction radiation of a charge moving near to a metallic grating. In the gravitational case, the role of the metallic grating is played by the inhomogeneities of the extra-dimensional space, such as a hidden brane. We derive a general formula for gravitational diffraction radiation and apply it to a higher-dimensional scenario with flat compact extra dimensions. Gravitational diffraction radiation may carry away a significant portion of the particle's initial energy. This allows to set stringent limits on the scale of brane perturbations. Physical effects of gravitational diffraction radiation are briefly discussed., Comment: 5 pages, 2 figures, RevTeX4. v2: References added. Version to appear in Phys. Rev. D

We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock experiments support local position invariance. Together these results confirm the Einstein Equivalence Principle which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Recently discovered binary pulsar systems may provide additional tests. Future and ongoing experiments, such as the Gravity Probe B Gyroscope Experiment, satellite tests of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could constrain extensions of general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of gravitational theory via detailed measurements of the properties of gravitational waves.

It is shown that the gravitational ultrarelativistic spin-orbit interaction violates the weak equivalence principle in the traditional sense. This fact is a direct consequence of the Mathisson-Papapetrou equations in the frame of reference comoving with a spinning test particle. The widely held assumption that the deviation of a spinning test body from a geodesic trajectory is caused by tidal forces is not correct, 12 pages

Gravitational waves were predicted by Einstein's general relativity. Up to now there has been no direct evidence for gravitational waves. Since the 1990's, laser interferometers have become the dominant detectors for gravitational wave detection, LIGO, Virgo, GEO600 and TAMA300 are the major laser interferometer gravitational wave observatories in the world. Chinese scientists would like to join the international club on gravitational wave detection and proposed a plan to build an underground China Einstein gravitational wave observatory (CEGO). As a preliminary stage, China plans to set up a 2/spl times/100 m prototype interferometer in Beijing.

We study the gravitational field of a spinning radiation beam-pulse in a higher dimensional spacetime. We derive first the stress-energy tensor for such a beam in a flat spacetime and find the gravitational field generated by it in the linear approximation. We demonstrate that this gravitational field can also be obtained by boosting the Lense-Thirring metric in the limit when the velocity of the boosted source is close to the velocity of light. We then find an exact solution of the Einstein equations describing the gravitational field of a polarized radiation beam-pulse in a space-time with arbitrary number of dimensions. In a $D-$dimensional spacetime this solution contains $[D/2]$ arbitrary functions of one variable (retarded time $u$), where $[d]$ is the integer part of $d$. For the special case of a 4-dimensional spacetime we study effects produced by such a relativistic spinning beam on the motion of test particles and light., 17 pages, 6 figures, published version

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein provided the framework for understanding modern astrophysical phenomena. Conversely, astrophysical observations provide one of the most effective means for testing Einstein's theories. Here, I review astrophysical advances precipitated by Einstein's insights, including gravitational redshifts, gravitational lensing, gravitational waves, the Lense-Thirring effect, and modern cosmology. A complete understanding of cosmology, from the earliest moments to the ultimate fate of the universe, will require developments in physics beyond Einstein, to a unified theory of gravity and quantum physics., Comment: 6 pages, 4 figures (resol. Reduced to 85 dpi)

The status of experimental tests of general relativity and of theoretical frameworks for analysing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational-wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible., Comment: 89 pages, 8 figures; an update of the Living Review article originally published in 2001; final published version incorporating referees' suggestions

There is only one experimental proof that gravitational waves exist. With such a limitation, it may seem premature to suggest the possibility that gravitational waves can became a preferred space propulsion technique. The present understanding of the problem indicates that this is not the case. The emission of gravitational waves from astrophysical sources has been confirmed by observation, the respective detection at large distance from the source is difficult and actually we have no confirmation of a successful detection. Therefore the required preliminary discovery has been already made. This opinion is enforced by many different proposals for building the required powerful gravitational wave generators that have recently appeared in the literature and discussed at conferences. It is no longer reasonable to wait for additional confirmation of the existence of gravitational waves to start a program for building generators and testing their possible application to space travel. A vast literature shows that gravitational waves can be employed for space propulsion. Gravitational wave rockets have been proposed, non‐linearity of Einstein equations allows the conversion of gravitational waves to a static gravitational field and “artificial gravity assist” may become a new way of travelling in space‐time. Different approaches to gravitational wave propulsion are reviewed and compared. Gravitational wave propulsion is also compared to traditional rocket propulsion and an undeniable advantage can be demonstrated in terms of efficiency and performance. Testing the predictions will require gravitational wave generators with high power and wavelength short enough for producing high energy densities. Detectors designed for the specific application must be developed, taking into account that non‐linearity effects are expected. The study and development of Gravitational wave propulsion is a very challenging endeavor, involving the most complex theories, sophisticated materials and testing techniques ever conceived by science. The development of Gravitational wave propulsion appears to be within the reach of a large national or a worldwide research program.

The motion of a cosmic 3 K radiation detector in a gravitational field is investigated in the context of general relativity. It is pointed out that solar gravity affects the measurements of the energy flux of radiation on an Earth detector and also that it causes a shift of about 0.6% on the maximum detected signal on an Earth device, in comparison to the prediction of special relativity.