According to Newton’s theory of gravity, the escape velocity v from a distance r from the center of gravity of a heavy object with mass m, is described by
1 2v2 = Gm r
What happens if a body with a large mass m is compressed so much that the escape velocity from its surface would exceed that of light, or, v > c? Are there bodies with a mass m and radius R such that 2Gm Rc2 ≥1 ? (1.2) This question was asked as early as 1783 by John Mitchell. The situation was investigated further by Pierre Simon de Laplace in 1796. Do rays of light fall back towards the surface of such an object? One would expect that even light cannot escape to inﬁnity. Later, it was suspected that, due to the wave nature of light, it might be able to escape anyway. Now, we know that such simple considerations are misleading. To understand what happens with such extremely heavy objects, one has to consider Einstein’s theory of relativity, both Special Relativity and General Relativity, the theory that describes the gravitational ﬁeld when velocities are generated comparable to that of light. Soon after Albert Einstein formulated this beautiful theory, it was realized that his equations have solutions in closed form. One naturally ﬁrst tries to ﬁnd solutions with maximal symmetry, being the radially symmetric case. Much later, also more general solutions, having less symmetry, were discovered. These solutions, however, showed some features that, at ﬁrst, were diﬃcult to comprehend. There appeared to be singularities that could not possibly be accepted as physical realities, until it was realized that at least some of these singularities were due only to appearances. Upon closer examination, it was discovered what their true physical nature is. It turned out that, at least in principle, a space traveller could go all the way in such a “thing” but never return. Indeed, also light would not emerge out of the central region of these solutions. It was John Archibald Wheeler who dubbed these strange objects “black holes”. Einstein was not pleased. Like many at ﬁrst, he believed that these peculiar features were due to bad, or at least incomplete, physical understanding. Surely, he thought, those crazy black holes would go away. Today, however, his equations are much better understood. We not only accept the existence of black holes, we also understand how they can actually form under various circumstances.