We describe a new analytic approach to the problem of black-hole oscillations, which has been investigated numerically thus far. Our treatment is based on a connection between the quasinormal modes and the bound states of the inverted black-hole effective potentials. Approximate analytic formulas for the quasinormal frequencies of Schwarzschild, Reissner-Nordström, and slowly rotating Kerr black holes are provided. We find that a real quasinormal frequency for an extreme Kerr black hole has vanishing amplitude in the ordinary (i.e., nonsuperradiant) regime; therefore, extreme Kerr black holes are not marginally unstable in this case. These results are significant for the question of the stability of a black hole as well as for the late-time behavior of radiation from gravitationally collapsing configurations.

The physical basis for the description of phenomena by a rotating observer is investigated. A simple, yet tentative, extension of the hypothesis of locality is used to determine the interference phase shift induced by the rotation of a neutron interferometer. The result consists of the Sagnac term, which is due to the coupling of the orbital angular momentum of the neutron with the rotation of the frame, and a new term which arises from a similar coupling because of the neutron spin. The latter effect is generally smaller than the Sagnac phase shift by the ratio of de Broglie wavelength of the neutron to the dimension of the interferometer. The possibility of detecting the new effect is briefly discussed.

The problem of propagation of electromagnetic waves in a gravitational field can be reduced to the problem of wave propagation in a material medium in flat space-time. This method is used here to calculate the scattering cross section of a Schwarzschild black hole and the polarization of the scattered wave. It is shown that the polarization of the wave (as measured at infinity) is not affected by the presence of the spherically symmetric gravitational field of the black hole. The light scattered from a rotating or "live" black hole is, however, expected to be polarized for an incident unpolarized plane wave. This may offer a new way to detect a live black hole.

The 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. The equations of motion of a light ray are solved in the first post-Minkowskian approximation which is linear with respect to the universal gravitational constant G. We do not restrict ourselves to the approximation of a gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of the source of light and the observer. This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of the pulsar and its companion. We also derive the correction to the light deflection angle caused by the 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.

A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general relativity but in the presence of “dark matter” that can be simply expressed as an integral transform of matter. It is shown that this approach can accommodate the Tohline–Kuhn treatment of the astrophysical evidence for dark matter