buy droppers get money maybe beat high score INTRODUCTION TO THE THEORY OF BLACK HOLES By Gerard ’t Hooft 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 2 v 2 = G m r . (1.1) 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 2G m R c2 ≥ 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 traveler could go all the way in such a “thing” but never return. Link https://webspace.science.uu.nl/~hooft101/lectures/blackholes/BH_lecturenotes.pdf
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