### Characteristic evolution and matching.

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The geodesic deviation equations, called also the Jacobi equations, describe only the first-order effects, linear in the small parameter characterizing the deviation from an original worldline. They can be easily generalized if we take into account the higher-order terms. Here we derive these higher-order equations not only directly, but also from the Taylor expansion of the variational principle itself. Then we show how these equations can be used in a novel approach to the two-body problem in...

Neutron stars may emit steady gravitational wave signals that will be among the first kinds of gravitational wave signals that the new generation of interferometric detectors will search for. I consider here the possibility that accreting neutron stars may be driven into the steady emission of gravitational waves. I estimate the amplitudes that the waves may have if the accretion takes place at the Eddington limit, such as may happen when a neutron star spirals inside a giant star in the endphase...