Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of general relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6601.8±18.3  mas/yr and a frame-dragging drift rate of -37.2±7.2  mas/yr, to be compared with the GR predictions of -6606.1  mas/yr and -39.2  mas/yr, respectively ("mas" is milliarcsecond; 1  mas=4.848×10(-9)  rad).

We generalize previous calculations to a fully relativistic treatment of adiabatic oscillations that are trapped in the inner regions of accretion disks by non-Newtonian gravitational e †ects of a black hole. We employ the Kerr geometry within the scalar potential formalism of Ipser and Lindblom, neglecting the gravitational Ðeld of the disk. This approach treats perturbations of arbitrary stationary, axisymmetric, perfect Ñuid models. It is applied here to thin accretion disks. Approximate analytic eigenfunctions and eigenfrequencies are obtained for the most robust and observable class of modes, which corresponds roughly to the gravity (internal) oscillations of stars. The dependence of the oscillation frequencies on the mass and angular momentum of the black hole is exhibited. These trapped modes do not exist in Newtonian gravity, and thus provide a signature and probe of the strong-Ðeld structure of black holes. Our predictions are relevant to observations that could detect modulation of the X-ray luminosity from stellar mass black holes in our Galaxy and the UV and optical luminosity from supermassive black holes in active galactic nuclei.

We compare our calculations of the frequencies of the fundamental g-, c-, and p-modes of relativistic thin accretion disks with recent observations of high-frequency quasi-periodic oscillations (QPOs) in X-ray binaries with black hole candidates. These classes of modes encompass all adiabatic perturbations of such disks. The frequencies of these modes depend mainly on the mass and angular momentum of the black hole; their weak dependence on disk luminosity is also explicitly indicated. Identifying the recently discovered, relatively stable QPO pairs with the fundamental g-and c-modes provides a determination of the mass and angular momentum of the black hole. For GRO J1655Ϫ40, and , in agreement with spectroscopic mass

We Ðrst brieÑy review how we investigate the modes of oscillation trapped within the inner region of accretion disks by the strong-Ðeld gravitational properties of a black hole (or a compact, weakly magnetized neutron star). Then we focus on the "" corrugation ÏÏ (c-) modes, nearly incompressible perturbations of the inner disk. The fundamental c-modes have eigenfrequencies (ordered by radial mode number) which correspond to the Lense-Thirring frequency, evaluated at the outer trapping radius of the mode, in the slow rotation limit. This trapping radius is a decreasing function of the black hole angular momentum, so a signiÐcant portion of the disk is modulated only for slowly rotating black holes. The eigenfrequencies are thus strongly increasing functions of black hole angular momentum. The dependence of the eigenfrequencies on the speed of sound (or the luminosity) within the disk is very weak, except for slowly rotating black holes.

The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.