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UT AST 309N - Review for Test #2

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Astronomy Bizarre Wheeler309N, Spring 2004 February 24, 2004(45005)Review for Test #2BLACK HOLESHistory – Mitchell, Laplace, escape velocity.Newton’s Theory of Gravity – force acts as if between centers of spherical objectsEinstein’s Theory of Gravity – based on simple Equivalence Principle: freely falling elevator equivalent to nogravity; accelerating elevator equivalent to gravity.Einstein says there is no “force” of gravity. Matter curves space and curved space tells matter how to move.Parallel propagation – straight lines in flat or curved space.Einstein says the space around a gravitating object (Earth, a star, a black hole) is curved in the same sense as a conepoked in a rubber sheet. The circumference of a circle drawn around such an object is less than 2π times the radiusand “straight lines,” the shortest distance between two points, curve around the object. One type of straight line inthis kind of curved space follows the curved space and closes on itself. An orbit is interpreted as this kind ofstraight line.Space versus Hyperspace – embedding diagramsEinstein says space around gravitating object “flows” inward, cause of free fall inward.E=mc2 – energy has weight, pressure to resist gravity can be self-defeatingEvent Horizon —Since nothing with velocity less than or equal to the speed of light can pass backward through anevent horizon, the information that an event occurred cannot pass through, so an event on the wrong side of anevent horizon can never be known to an observer on the opposite side, hence the name.Schwarzschild Radius—the distance of the event horizon from the center of a black hole. For a non-rotating, non-charged, black hole the radius of the event horizon is 3 kilometers x (mass/solar mass) i.e. if the Sun were a blackhole its event horizon would be 3 kilometers in radius (the Sun is actually about a million kilometers in radius).Singularity—region in center of black hole where ordinary space and time cannot exist because of severe spacetime curvature and quantum uncertainty. The boundary of physics as we currently know it.Tidal forces tend to draw any object into a “noodle” shape for two reasons: the force closer to the center isstronger and because two separated points the same distance from the hole tend to approach one another as theyboth try to fall directly toward the center.Einstein says that all objects accelerate at the same rate near a gravitating object because that object curves the spacearound it and everything falls on the same “straight” line, independent of their own nature.Far away from a gravitating object, space is “flat” and there is no gravity. Black holes are “safe” from a distance.Nature of Time in the vicinity of a black hole. Any observer always senses his or her own time as perfectlynormal. But an observer at a large distance from the black hole where the force of gravity is small sees timepassing more slowly for events occurring deep in the gravitational field of a black hole. Events right at the eventhorizon would show no passage of time to a distant observer. A distant observer watching another person fallingtoward the event horizon would perceive (other effects not interfering) that this second person graduallyapproached but never crossed the event horizon. An observer freely falling under the influence of no forces wouldplunge into the black hole after a finite (and normally short) passage of their own time.Redshift—the redshift of the wavelength of photons received at a distance gets very large as the point of emissionof the photon gets more deep in a gravitational field.“Black Hole”—the large redshift of photons emitted near the event horizon coupled with the long passage of timebetween the arrival of these photons at a distant observer due to the apparent slowing of time means that eventshappening just outside the event horizon cannot, in practice, be “seen” by a distant observer—hence, “black hole”is a more accurate term than “frozen star” which does not connote the blackness.Temperature of a black hole—according to Stephen Hawking, if one studies the event horizon with the QuantumTheory one finds that the gravitation energy (and hence mass) of a black hole can be converted into matter and anti-matter (mostly photons) with some of this material being ejected carrying off the mass of the hole.Black Hole Evaporation—For a black hole of ordinary stellar mass or larger the amount of mass loss is negligiblein the age of the Universe and may be ignored. A black hole of less than asteroid size could totally evaporatewithin the age of the Universe.Time-like space—interior to event horizon space drags in one direction, just as time drags you older.Schwarzschild black hole—mass but no spin, no


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