No abstract

The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R^{-1}, where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R^{-2}, and it is carried out through order R^{-4}. The metric is parameterized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate $v$ is constant on past light cones that converge toward the black hole; the angles theta and phi are constant on the null generators of each light cone; and the radial coordinate r is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: r = 2M. At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the black-hole surface area increases as a result of the tidal interaction.Comment: 43 pages, 2 figure

The most precise test of the post-Newtonian γ parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field of the Sun, generated by its barycentric orbital motion, on the Shapiro delay. This non-stationary gravitational field of the Sun is associated with the Lorentz transformation of the metric tensor and the affine connection from the heliocentric to the barycentric frame of the solar system and can be treated as gravimagnetic field. The gravimagnetic field perturbs the propagation of a radio wave and contributes to its frequency shift at the level up to 4 × 10 −13 that may affect the precise measurement of the parameter γ in the Cassini experiment to about one part in 10,000. Our analysis suggests that the translational gravimagnetic field of the Sun can be extracted from the Cassini data, and its effect is separable from the space curvature characterized by the parameter γ.

First post-Newtonian (PN) approximation of the scalar-tensor theory of gravity is used to discuss the effacing principle in N-body system, that is dependence of equations of motion of spherically-symmetric bodies comprising the system on their internal structure. We demonstrate that the effacing principle is violated by terms which are proportional to the second order rotational moment of inertia of each body coupled with β − 1, where β is the measure of non-linearity of gravitational field. In case of general relativity, where β = 1, the effacing principle is violated by terms being proportional to the rotational moment of inertia of the forth order. For systems made of neutron stars (NS) and/or black holes (BH) these terms contribute to the orbital equations of motion at the level of the third and fifth PN approximation respectively.It is well-known that in the Newtonian physics as well as in general relativity the external gravitational field of an isolated body having non-rotating, sphericallysymmetric distribution of mass, does not depend on the specific internal structure of the body, and is completely determined by a single parameter that is mass of the body. This property of the gravitational field is called the effacing principle.

No abstract