rev.ex4.fall.11 - Cosmic Catastrophes 309N Fall 2011...

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Cosmic Catastrophes Wheeler 309N Fall 2011 November 7, 2011 ( 47580) Review for Test #4 Einstein’s Gravity, Black Holes and Gamma-Ray Bursts Embedding diagram – a method of reducing a three (or higher) dimensional space to two-dimensional space that preserves the basic geometry and curvature of the original space. This allows us to “see” the curvature. Einstein says the space around a gravitating object (Earth, a star, a black hole) is curved in the same sense as a cone poked in a rubber sheet. The circumference of a circle drawn around such an object is less than 2 π times the radius and “straight lines,” parallel propagated, the shortest distance between two points, curve around the object. One type of straight line in this kind of curved space follows the curved space and closes on itself. An orbit is interpreted as this kind of straight line. Event Horizon – Since nothing with velocity less than or equal to the speed of light can pass backward through an event horizon, the information that an event occurred cannot pass through, so an event on the wrong side of an event horizon can never be known to an observer on the opposite side, hence the name. Singularity – region in center of black hole where ordinary space and time cannot exist because of severe space time 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 is stronger and because two separated points the same distance from the hole tend to approach one another as they both try to fall directly toward the center. 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 perfectly normal. But an observer at a large distance from the black hole where the force of gravity is small sees time passing more slowly for events occurring deep in the gravitational field of a black hole. Events right at the event horizon would show no passage of time to a distant observer. A distant observer watching another person falling toward the event horizon would perceive (other effects not interfering) that this second person gradually approached but never
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This note was uploaded on 11/13/2011 for the course AST 309N taught by Professor Wheeler during the Fall '11 term at University of Texas at Austin.

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rev.ex4.fall.11 - Cosmic Catastrophes 309N Fall 2011...

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