So what's so special about Special Relativity? The answer is that it assumes that there is no gravitational forces. It took Einstein 12 more years to devise a General Theory of Relativity which included the force of gravity. Only once the General Theory was worked out could the details of objects with escape velocities as great as the speed of light be fully grasped.

In essense, General Relativity says that matter "curves" space and time, and that it is this curvature that changes the direction of moving objects. Thus, rather than describing gravity as a force exerted by a massive object on some other object, Einstein described gravity as a warp in space and time, which in turn affects the motion of objects in motion. A more detailed explanation is given by Thorne in this weeks readings.

Karl Schwarzschild provided a particular solution to Einstein's equations of General Relativity that was appropriate for spacetime near a spherical object with escape velocities larger than the speed of light. This solution demonstrated that an imaginary spherical surface called the "Event Horizon" surrounds such an object. This surface is placed at a radius where the escape velocity is precisely equal to the speed of light. This radius has come to be called the "Schwarzschild radius". It can be calculated in our (link popup window: "http://nuna.its.yale.edu/~blakhole/") *escape velocity calculator* by setting the escape velocity equal to the speed of light.

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The Event Horizon is so called because an event that occurs inside it can never be detected in the outside world. Thus the behavior of matter and energy inside the Event Horizon cannot be verified by any conceivable experiment. We can make the assumption, however, that Einstein's equations hold in the same form inside the Event Horizon as they do outside in our ordinary Universe. This assumption is the basis of many of the (link popup window: spacetime_reversed.html) *mind-boggling descriptions* of what black holes can do. But it is important to remember that all such speculations rest on an untestable assumption, namely that Einstein's equations hold inside the Event Horizon.

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A full description of General Relativity is out of the scope of this course but we encourage those interested to go to the (link popup window: http://archive.ncsa.uiuc.edu/Cyberia/NumRel/NumRelHome.html) *Spacetime Wrinkles* and (link popup window: http://physics.syr.edu/courses/modules/LIGHTCONE/index.html) *The Light Cone* web pages. Please also read pages ?? to ?? of Kip Thorne's book "Blackholes and Timewarps: Einstein's Outrageous Legacy".