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Celebrating Einstein
“The General Theory of Relativity”


F.  Black Holes

The effects of spacetime curvature on light, on time, on distance, and on spinning objects can all be seen in the familiar gravitational fields of the earth and the solar system.  General relativity implies the existence of some even more intriguing phenomena, associated with the extremely intense gravitational fields known as black holes.

Outside a black hole, spacetime has the same kind of shape that we find around a massive object, but within, the shape of spacetime takes an interesting turn.  There, the direction of time has traded places with the inward direction of space.  An object inside the black hole that followed the straightest possible path in spacetime—the path of gravitational attraction—would find the direction of its future pointing ever inward, and never toward the outside of the hole.

In fact, if matter behaved according to the expectations of 19th-century physicists, it would be strictly impossible for the object to ever escape.  Even if a force were applied to counter gravity and "unstraighten" the object's path, it still couldn't leave; in effect, the escape velocity from a black hole's interior is larger than the speed of light.  The region outside the black hole does have an achievable escape velocity, since the directions of spacetime there are the same as they are outside an ordinary object.

Black holes don't suck matter in; they're more like trapdoors in space than vacuum cleaners.  But the trapdoor is evidently not an absolute one, because matter has some properties that physicists only began to recognize at the close of the 19th century.  By taking account of these properties, Steven Hawking showed in 1974 that matter should slowly leak out of black holes all the time.  It turns out that the rate of escape from a black hole is inversely proportional to the hole's surface area, which will shrink as more matter escapes.  A large black hole thus emits matter and shrinks slowly, but given enough time it will become small enough to emit matter and shrink much more rapidly.

The general theory of relativity has come a long way from its early days, when only a few people in the world understood it.  Nowadays a typical class introduced to the details of general relativity will have something like a dozen students, and many such classes are conducted each year in schools all over the world.  It took physicists a while to get used to a theory of curved spacetime, and to the mathematics needed to describe and reason about the curvature.  Over the last nine decades, advanced in telescopes and experimental devices have made it possible to see more evidence of spacetime curvature in nature, and progress with computers and software has made it feasible to calculate implications of the theory that were once impractically hard to work out.

References, Links, and Comments:

With this article we come full circle, from Einstein's special relativity theory of interrelated space and time, to his general theory of curved spacetime.  Many of the references and links at the end of the earlier article deal with both installments of the relativity theory, and are thus repeated here.

Some other references on the general theory include:

Additional links related to specific topics mentioned above:

"The Weight of Light”, Physical Review Focus, 12 July 2005.
The story of the tower experiments by Pound, Rebka, and Snider.

"Gravity Probe B:  Testing Einstein’s Universe"
Stanford University's official website for the satellite gyroscope experiment described above.  (Gravity Probe A was the hydrogen maser clock sent on a rocket flight in 1976 to measure the difference in time flow between the rocket's flight path and the ground.)

"An introduction to general relativity, Spaceflight Now
Describes several features of curved spacetime, with emphasis near the end on Gravity Probe B.

What goes up need not come down, if it can rise quickly enough.  While the spacetime curvature associated with any object can extend throughout the universe, this curvature is smaller at greater distance from the object.  In other words, an object's gravitational attraction is weaker, the further one is from the object.  So while anything will be decelerated by gravity as it rises, if its initial speed is fast enough then gravity will never slow it enough to reverse its course.  The speed required to avoid falling back towards an attracting object is called that object's escape velocity.

The lunar hammer-feather drop experiment is described on several websites, including:
"The legend of the leaning tower", by Robert P. Crease, physicsweb
"The Apollo 15 Hammer-Feather Drop", author/curator Dr. David R. Williams, NASA
     8.3 megabyte QuickTime movie
"A Brief History of the Exploration of the Moon", by Mark R. Whittington



Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information 

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