Gravitational Waves and Black Holes - the Legacy of General Relativity

While the Newtonian theory of gravity is similar to electrostatics, the field equations in both cases being elliptic, Einstein's general relativity is more similar to Maxwell's electromagnetic theory, the field equations in both cases being of hyperbolic character. A consequence of this fact is the presence in general relativity of gravitational waves, which are analogous to electromagnetic waves. Due however to the nonlinear nature of Einstein's equations, a long time elapsed before the theory of gravitational waves reached a satisfactory level of understanding. Another fundamental feature of general relativity is that gravitational collapse leads to the formation of spacetime regions which are inaccessible to observation from infinity, the black holes. In the last two years, on several occasions, wave trains have been detected generated by binary black holes which inspiral and coalesce. In my lecture, I shall describe the basic concepts, give an outline of their historical development, and discuss how the theory connects to the recent observations.