Einstein's paper on gravitational waves was published in 1916, and that was about all that was heard on the subject for over forty years. It was not until the late 1950s that some relativity theorists, H. Bondi in particular, rigorously proved that gravitational radiation was in fact a physically observable phenomenon, that gravitational waves carry energy, and that as a result a system that emits gravitational waves should lose energy.
In Newton's theory of gravity, the gravitational interaction between two bodies is instantaneous. According to Special Relativity, however, this should be impossible, because the speed of light represents the limiting speed for all interactions. If a body changes shape, the resulting change in the force field will make its way outward at the speed of light. It is interesting to note that already in 1805, Laplace, in his famous Traité de Mécanique Céleste, stated that if gravitation propagates with finite speed, the force in a binary star system should not point along the line connecting the stars, and the angular momentum of the system must slowly decrease with time. Today we would say that this happens because the binary star is losing energy and angular momentum by emitting gravitational waves. It was 188 years later, in 1993, that Hulse and Taylor were awarded the Nobel Prize for Physics for their indirect proof of the existence of gravitational waves using exactly this kind of observation of the binary pulsar PSR 1913+16. A direct detection of gravitational waves has still not been achieved to this day.
General Relativity replaces the Newtonian picture of gravitation by a geometric one that is very intuitive, if we are willing to accept the fact that space and time do not have an independent existence, but rather are in intense interaction with the physical world. Massive bodies produce 'indentations' in the fabric of spacetime, and other bodies move in this curved spacetime taking the shortest path, much like a system of billiard balls on a springy surface. In fact, the Einstein field equations relate mass (energy) and curvature in much the same way that Hooke's law relates force and spring deformation, or phrased somewhat poignantly: spacetime is an elastic medium.
The nature of gravitational waves
If a mass distribution moves in an asymmetric way, then the spacetime indentations travel outwards as ripples in spacetime called 'gravitational waves'. Gravitational waves are fundamentally different from the familiar electromagnetic waves. While electromagnetic waves, created by the acceleration of electrical charges, propagate in the framework of space and time, gravitational waves, created by the acceleration of masses, are waves of the spacetime fabric itself.
Unlike charge, which exists in two polarities, masses always come with the same sign. This is why the lowest order asymmetry producing electromagnetic radiation is the dipole moment of the charge distribution, whereas for gravitational waves it is a change in the quadrupole moment of the mass distribution. Hence those gravitational effects that are spherically symmetric will not give rise to gravitational radiation. A perfectly symmetrical collapse of a supernova will produce no waves, while a non-spherical one will emit gravitational radiation. A binary system will always radiate. Gravitational waves distort spacetime: in other words, they change the distances between free macroscopic bodies.
A gravitational wave passing through the Solar System creates a time-varying strain in space that periodically changes the distances between all bodies in the Solar System in a direction that is perpendicular to the direction of wave propagation. This could be the distance between a spacecraft and the Earth, as in the case of Ulysses or Cassini (attempts have been and will be made to measure these distance fluctuations), or the distances between shielded proof masses inside spacecraft that are separated by a large distance, as in the case of LISA. The main problem is that the relative length change due to the passage of a gravitational wave is exceedingly small. For example, the periodic change in distance between two proof masses, separated by a sufficiently large distance, due to a typical white dwarf binary at a distance of 50 pc (about 1500 billion km, or 160 light years) is only 10 -10 m. This is not to say that gravitational waves are weak in the sense that they carry little energy. On the contrary, a supernova in a not too distant galaxy will drench every square metre here on Earth with kilowatts of gravitational radiation. The resulting length changes are, however, very small because spacetime is an extremely stiff elastic medium, so that it takes extremely large energies to produce even minute distortions.
(Extract from LISA: Detecting and observing gravitational waves, the Mission Summary of the Cornerstone Study Results, ESA brochure 164.)