Bahram Mashhoon

On the Gravitational effects of rotating masses - The Thirring-Lense Papers

The purpose of this work is to provide a critical analysis of the classical papers of H. Thirring [Phys. Z.,19, 33 (1918);Phys. Z.,22, 29 (1921)] and J. Lense and H. Thirring [Phys. Z.,19, 156 (1918)] on rotating masses in the relativistic theory of gravitation and to render them accessible to a wider circle of scholars. An English translation of these papers is presented which follows the original German text as closely as possible. This is followed by a concise account of the significance of the results of these papers as well as the possibility of measuring the gravitational effects of rotating masses.

Gravitational effects of rotating masses

A gyroscope in orbit about a central rotating mass undergoes relativistic nutational oscillations in addition to the well-known precessional motions. The amplitude of the oscillation is proportional to the angular momentum of the rotating mass and its period is the Fokker period of geodetic precession. The amplitude is maximum for a polar orbit and vanishes if the orbit is equatorial. This nodding effect is due to a small divisor phenomenon involving the Fokker frequency, and its existence implies that the applicability of the post-Newtonian approximation of general relativity is limited in time. The dynamical significance of the new effect for the relative motion of neighboring test masses in the field of a rotating mass as well as for the restricted three-body problem in general relativity is investigated and the possibility of its detection is briefly discussed.

general covariance and quantum theory

The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory.

Exterior gravitational field of a rotating deformed mass

Abstract We obtain a new solution of the vacuum Einstein equations by means of the rank-zero Hoenselaers-Kinnersley-Xanthopoulos transformations. We take as seed metric the static axisymmetric Erez-Rosen metric, which describes the exterior field of a mass with arbitrary quadrupole moment. The Ernst potential of the new solution is presented and all metric functions are explicitly given. The new metric, which contains the Kerr and Erez-Rosen metrics as special cases, represents the exterior gravitational field of a rotating mass with arbitrary quadrupole moment.

Quasi-normal oscillations of a schwarzschild black hole

Abstract The modes of oscillation of a Schwarzschild black hole are determined within an analytic framework. These quasi-normal modes are related to the bound states of the inverted black hole potential which is approximated by the inverted Eckart potential. For a given angular momentum parameter j , the real part of the quasi-normal frequency decreases as the mode number n (or, equivalently, the damping factor) increases, in agreement with the results of numerical studies.

Gravitational influence of the rotation of the sun on the earth-moon system

Abstract A new approach to the relativistic theory of the motion of the moon is presented. In this framework, the contribution of the gravitational “magnetic” field of the sun to the tidal force acting on the earth-moon system is determined. Furthermore, the main relativistic perturbations in the lunar motion are estimated.

On a new gravitational effect of a rotating mass

A new general relativistic many-body effect is described. It results in an unexpectedly large relative acceleration between neighboring test particles that follow an inclined orbit about a rotating mass. The effect vanishes if the orbit coincides with the equatorial plane of the rotating mass. The existence of this effect is due to a small divisor involving the deviation of the orbital frequency measured by a comoving clock from the frequency measured by an inertial clock. The influence of the rotation of the Sun on the Earth-Moon system is investigated, and it is shown that the new effect causes a harmonic variation in the Earth-Moon separation with an amplitude of order 1 m and dominant periods of 18.6 yr, ∼1/2 yr, 1 month, and ∼1/2 month. The confirmation of these results by the lunar laser ranging experiment would provide a significant new test of general relativity and a measurement of the angular momentum of the Sun.

Is the Universe Homogeneous on a Large Scale

The present standard model of cosmology is based on the cosmological principle which has only limited observational support, especially in connection with the issue of large-scale homogeneity. The recent discovery of voids provides further impetus for the study of large-scale inhomogeneities. It is proposed to replace the hypothesis of spatial homogeneity by the assumption that the (matter and radiation) content of the universe is on the average uniform, i.e., the equation of state of the system is everywhere the same. It has been shown that if (a) the universe is spatially isotropic, (b) the content of the universe is approximated on the average by a perfect fluid obeying a physically reasonable equation of state p = p(μ), including p = O, and (c) the expansion or contraction of the universe is shear-free, then the only physically acceptable nonstatic cosmological solution of the EinsteinMaxwell equations is the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. If (c) is relaxed, then Einstein’s equations allow solutions which differ from the FLRW models by the existence of radial inhomogeneities due to shear. As a first step toward a general study of inhomogeneities, local models with radial inhomogeneities have been developed and the observational quantities for such models have been determined.