Scattering by Black Holes

Black holes, objects so compact that not even light can escape their gravitational pull, are among the most intriguing concepts of modern science. As Kip Thorne wrote in 1974: “Of all the conceptions of the human mind from unicorns to gargoyles to the hydrogen bomb perhaps the most fantastic is the black hole: a hole in space with a definite edge over which anything can fall and nothing can escape; a hole that curves space and warps time.” Evidence that these exotic objects exist in our universe has been mounting since the discovery of the archetypal black hole Cygnus X1 in 1971. Today, the presence of supramassive black holes (several million times as massive as our sun) at the centre of many galaxies, and smaller black holes (5-10 times as massive as the sun) in X-ray binary systems, is generally accepted. From the mathematical point of view, a black hole is a spacetime defined by a four-dimensional metric tensor, that is, a solution of Einstein’s equations, with characteristic properties. The simplest black hole is spherically symmetric and non-rotating. It is known as the Schwarzschild black hole, and is described by the metric tensor gab which is given by