Gravitational redshift of gravitational clocks

The gravitational redshift of gravitational clocks in a given weak gravitational field, within general relativity, is considered. Because the clocks in question have structure and dynamics determined by gravitational interactions, the full machinery of Einstein's equations must be used. Three specific examples are treated: (i) the redshift of the angular frequency of a rotating relativistic star in the gravitational field of a distant body; (ii) the redshift of the angular velocity of a slowly rotating black hole surrounded by an axisymmetric ring of matter; and (iii) the redshift of the observed orbital period of a nearly circular, post-Newtonian binary system in the field of a distant, third body. In all three cases the redshift is the same as if the clocks were non-gravitational, thereby governed by the Einstein equivalence principle. For an observer at infinity, the redshift $\text{Z ≡}\text{Δv}\text{v}$ is given by $\text{Z =}\text{?Gm}\text{Rc}{}^2$, where m is the mass of the distant object and R its distance from the clock in question. The result is independent of how relativistic the clock may be. The significance of this conclusion for the binary pulsar PSR 1913 + 16, where the gravitational redshift of the pulsar's frequency caused by the gravitational field of its companion is an observable effect, is discussed. The extent to which this result is a manifestation of the strong equivalence principle, satisfied, as far is known, only by general relativity, is also noted.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

Magnetized neutron-star mergers and gravitational-wave signals

We investigate the influence of magnetic fields upon the dynamics of, and resulting gravitational waves from, a binary neutron-star merger in full general relativity coupled to ideal magnetohydrodynamics. We consider two merger scenarios: one where the stars have aligned poloidal magnetic fields and one without. Both mergers result in a strongly differentially rotating object. In comparison to the nonmagnetized scenario, the aligned magnetic fields delay the full merger of the stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal magnetic fields. These effects not only mediate the production of electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves.     

No black holes: A gravitational gauge theory possibility

The most general lowest order lagrangian that can be formed from gauge-derived vierbein invariants is constrained by the hypothesis that the speed of light as measured by conventional rods and clocks of atomic constitution is independent of direction in a gravitational field. It is shown that the standard weak field observational tests of general relativity serve to eliminate all possible combinations of parameters in this constrained lagrangian except two. One parameter choice gives the isotropic Schwarzchild black hole metric of the general theory of relativity. The other allowable choice leads to an exponential metric of the class proposed by Yilmaz, corresponding in strong fields to large red shifts without black hole formation.     

Boundary terms in the action for the Regge calculus

The boundary terms in the action for Regge's formulation of general relativity on a simplicial net are derived and compared with the boundary terms in continuum general relativity.Supported in part by the National Science Foundation grants PHY 78-09620 and PHY 78-24275.     

Lorentz-Covariant theory of gravitation

A Lorentz-covariant theory of gravitation is proposed. It is based on a simple form of the Lagrangian for the gravitational field. The field equations have a simple mathematical structure where the energy-momentum tensor of matter and of gravitational field is the source of the field. The theory agrees with general relativity for the three well-known effects, i.e., red shift, deflection of light, and perihelion.     

Are there geon analogues in sourceless gauge-field theories?

It has recently been shown that there is no finite-energy non-singular solution to the sourceless gauge-field equations in four-dimensional Minkowski space that does not radiate energy. However, this does not preclude the possibility of solutions which hold themselves together for a long time before radiating away their energy. If they existed, such objects would be analogous to the geons of general relativity. We show such objects do not exist.Work supported in part by the National Science Foundation under Grants No. PHY75-20427 and No. PHY76-14852Junior Fellow, Society of Fellows     

Interaction,not gravitation

Cannon and Jensen assert that data from different national time laboratories give a test of the interaction interpretation of special relativity theory. That interpretation is to be applied, however, to clocks in relative uniform motion, and therefore is not tested by the time-rate effects associated with different terrestrial locations of clocks. Those effects are described by the general theory of relativity, and arise with differences in gravitational potential and state of circular motion of the clocks. An argument by the authors against invariance of entropy clocks, on grounds of neglect of relativity of simultaneity, is also criticized.     

A new proof of the positive energy theorem

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau.) The relevance of these results to the stability of Minkowski space is discussed.Research partially supported by NSF Grant PHY78-01221     

Static spherically symmetric star in Gauss-Bonnet gravity

We explore static spherically symmetric stars in Gauss-Bonnet gravity without a cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of the red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of the red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can hold in Gauss-Bonnet gravity.     

Existence of dual mass: Linear theory

The field equations of general relativity are symmetrized in a manner similar to Dirac's symmetrization of electromagnetism. This symmetrization allows us to predict the existence of a gravitational, magnetic-like mass which we call dual mass. Time-independent solutions for both rotating and nonrotating sources are constructed for these generalized equations. The gravitational field produced by the dual mass source is compared with the gravitational field that follows from the linearized NUT and Kerr-NUT metrics, and an identification of the NUT parameter with a dual mass monopole is made.     

General Relativistic Shift in Plasma Frequency due to a Slowly Rotating Compact Star

We investigate the effects of a slowly rotating compact gravitational source on plasma oscillations using the gravitoelectromagnetic approximation to the general theory of relativity. It is shown that there is a shift in the plasma frequency and hence in the refractive index of the plasma due to the gravitomagnetic force. Estimates for the difference in frequency of radially transmitted electromagnetic signals are given for typical compact star candidates. The proposed shift provides a new test of general theory of relativity in the slow rotation approximation.     

广义相对论浅释(1)

本文用通俗的方法介绍了广义相对论的基本思想 ,并得到了史瓦西场时空弯曲的规律及质点在史瓦西场中自由运动的规律 ,从而解决了引力红移 ,CS原子钟环地球飞行后与地面上 CS原子钟的时差 ,行星进动 ,光子经过太阳表面时的偏转角 ,雷达回波延迟等问题 .     

Post-Newtonian approximation for a rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a rotating frame of reference. A new method of approximation is used based on a 3+1 decomposition of the equations. The results are expressed explicitly in terms of the gravitational potentials. The space-time is asymptotically flat but not locally flat. The space-time metric contains gravitational terms, inertial terms, and coupled gravitational-inertial terms. The inertial terms in the equation of motion are in agreement with terms obtained by other authors using kinematic methods. The metric and equation of motion reduce to those for an inertial frame of reference under a simple coordinate transformation. The total energy of a particle is given. For the restricted three-body problem this represents the relativistic extension of Jacobi's integral to post-Newtonian order.This article received an honorable mention from the Gravity Research Foundation for the year 1984—Ed.     

Numerical modeling of black holes as sources of gravitational waves in a nutshell

These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the concept of a well-posed initial value problem, the construction of initial data for general relativity, trapped surfaces and gravitational waves. Also, a brief summary is given of recent progress regarding the numerical evolution of black hole binary systems.     

Gravitational Effects in the Propagation and in the Emission of Light

Following Chou's viewpoint that the Cartesian system of space coordinates and timedefines a Minkowskian space-time in which Einstein's field equations and the harmonic conditionare the laws of gravitation (Ref.[1]), we study the effects of an external gravitational fieldin the propagation and in the emission of light respectively from the generalized Maxrwell andDirac equations of the general theory of relativity by geometric optics and quantum mechanics,and get the usual results for the red shift. For the naively homogeneous and isotropic model ofcosmology (the case with k = 0 in the Robertson-Walker scheme) closed form for the relationbetween distance and red shift is obtained, which indicates that a new way of analyzing theobservational data with not too small red shifts is needed.     

Using Hamilton-Jacobi Equation to Study the Neutrino Oscillations in the Stationary Space-Time

We study the mass neutrino oscillation by solving Hamilton-Jacobi equation in the Kerr-Newman-Kasuya space-time, as an important example of the stationary space-time, and give the general expression of the oscillation phase. A special case, the geodesic with L=aE is considered. Then, the proper oscillation length is studied carefully. The effects of the gravitational field, the rotating parameter a, the electric charge and magnetic charge on the oscillation length are given. It is worth noting that a blue shift of the oscillation length rather than a red shift takes place as the neutrino travels out of the gravitational field.     

Measurability analysis of the magnetic-type components of the linearized gravitational radiation field

Ambiguities of gravitational field measurements are resolved in the linearized version of general relativity. A potential energy of a mass quadrupole in a gravitational field is found which permits determination of the linearized Weyl tensor. AGedanken spin resonance experiment is devised to measure the magnetic-type components of the Weyl tensor; the experiment confirms the observability of these components when they are suitably averaged over a world domain.Work supported in part by National Science Foundation grant No. MPS 74-15246 to Syracuse University.     

The second-order gravitational redshift

It now appears possible that anotherdistinct test of the second-order term of general relativity may be feasible, through the use of very stable atomic clocks. This experiment, which would measure the second-ordergravitational redshift, is a bona fidetest of the field equations of gravity, not just a test of the underlying principle of equivalence.Presented at the Seventh International Conference on Gravitation and Relativity, June 1974, Tel-Aviv, IsraelResearch supported in part by NASA Research Grant NGR 09-015-205.     

An interaction interpretation of special relativity theory. Part II

The interaction interpretation of special relativity theory (elaborated in Part I) is discussed in relation to quantum theory. The relativistic transformations (Lorentz processes) of physical variables, on the interaction interpretation, are observation-interaction dependent, just as are the physical values (eigenvalues) of systems described by quantum-theoretic state functions; a common, basic structure of the special relativity and quantum theories can therefore be presented. The constancy of the light speed is shown to follow from interaction-transformations of frequency and wavelength variables. A parallelism is suggested between, on the one hand, the Lorentz-Clausius distinction for relativistic transformations, and, on the other, the distinction between observation-dependent and observation-independent natural processes. The empirical study of rates of macroscopic clocks can provide a critical test of the interaction interpretation and of a possible extension to gravitational time changes; the role of time as prior determinant of natural process is at issue. The Hafele-Keating observations are of general relativity effects on clocks in accelerated motion.