Gravity Probe A

Abstract: We perform numerical simulations of a three-dimensional (3D) time evolution of pure gravitational waves. We use a conformally flat and K=0 initial condition for the evolution of the spacetime. We adopt several slicing conditions to check whether a long time integration is possible in those conditions. For the case in which the amplitude of the gravitational waves is low, a long time integration is possible by using the harmonic slice and the maximal slice, while in the geodesic slice (\ensuremath{\alpha}=1) it is not possible. As in the axisymmetric case and also in the 3D case, gravitational waves with a sufficiently high amplitude collapse by their self-gravity and their final fates seem to be as black holes. In this case, the singularity avoidance property of the harmonic slice seems weak, so that it may be inappropriate for the formation problems of the black hole. By means of the gauge-invariant wave extraction technique we compute the waveform of the gravitational waves at an outer region. We find that the nonlinearity of Einstein gravity induces the higher multipole modes even if only a quadrupole mode exists initially.

Abstract: We have used a neutron interferometer to observe the quantum-mechanical phase shift of neutrons caused by their interaction with Earth's gravitational field.

Abstract: The rigorous solution for cylindrical gravitational waves is given. For the convenience of the reader the theory of gravitational waves and their production, already known in principle, is given in the first part of this paper. After encountering relationships which cast doubt on the existence of rigorous solutions for undulatory gravitational fields, we investigate rigorously the case of cylindrical gravitational waves. It turns out that rigorous solutions exist and that the problem reduces to the usual cylindrical waves in euclidean space.

Abstract: The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.