Simple Nature - Light and Matter

object that that isn’t influenced by anything other than gravity. Bythis definition, a free-falling rock defines an inertial frame, but thisbook sitting on your desk does not.m / Matter is lifted out of aNewtonian black hole with abucket. The dashed line representsthe point at which theescape velocity equals the speedof light. For a real, relativisticblack hole, this is impossible.7.4.3 Black holesThe observations described so far showed only small effects fromcurvature. To get a big effect, we should look at regions of space inwhich there are strong gravitational fields. The prime example is ablack hole. The best studied examples are two objects in our owngalaxy: Cygnus X-1, which is believed to be a black hole with aboutten times the mass of our sun, and Sagittarius A*, an object nearthe center of our galaxy with about four million solar masses.Although a black hole is a relativistic object, we can gain someinsight into how it works by applying Newtonian physics. A sphericalbody of mass M has an escape velocity v = √ 2GM/r, whichis the minimum velocity that we would need to give to a projectileshot from a distance r so that it would never fall back down. If ris small enough, the escape velocity will be greater than c, so thateven a ray of light can never escape.We can now make an educated guess as to what this meanswithout having to study all the mathematics of general relativity.In relativity, c isn’t really the speed of light, it’s really to be thoughtof as a restriction on how fast cause and effect can propagate throughspace. This suggests the correct interpretation, which is that for anobject compact enough to be a black hole, there is no way for anevent at a distance closer than r to have an effect on an event faraway. There is an invisible, spherical boundary with radius r, calledthe event horizon, and the region within that boundary is cut offfrom the rest of the universe in terms of cause and effect. If youwanted to explore that region, you could drop into it while wearinga space-suit — but it would be a one-way trip, because you couldnever get back out to report on what you had seen.In the Newtonian description of a black hole, matter could belifted out of a black hole, m. Would this be possible with a realworldblack hole, which is relativistic rather than Newtonian? No,because the bucket is causally separated from the outside universe.No rope would be strong enough for this job (problem 12, p. 440).One misleading aspect of the Newtonian analysis is that it encouragesus to imagine that a light ray trying to escape from a blackhole will slow down, stop, and then fall back in. This can’t be right,because we know that any observer who sees a light ray flying byalways measures its speed to be c. This was true in special relativity,and by the equivalence principle we can be assured that the same istrue locally in general relativity. Figure n shows what would reallyhappen.430 Chapter 7 Relativity