EXAM 3 Study Guide

EXAM 3 Study Guide - Relativity and Black Holes Understand...

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Relativity and Black Holes Understand the basis for Einstein's General Theory of Relativity: Any massive object causes space to curve and time to slow down, and these effects manifest themselves as a gravitational force. These distortions of space and time are most noticeable in the vicinity of large masses or compact objects - predicts a number of phenomena, including the bending of light by gravity and the gravitational redshift, whose existence has been confirmed by observation and experiment - Also predicts the existence of gravitational waves, and black holes O Why we need it (special relativity limitations) - Einstein’s Special Relativity: Two Postulates 1. All of the laws of physics (except gravitation) are the same for every inertial observer 2. The speed of light is the same constant, independent of the motion of the source -Does not include Gravitation o Equivalence principle significance (equality of inertial and gravitational mass) - As a consequence of the equality of gravitational and inertial mass you cannot distinguish (locally) between 1. Being at rest in a gravitational field (as in the surface of the Earth) and 2. Being accelerated upward in a gravity-free environment (non-inertial frame of reference) o Gravity is replaced by curvature of space-time. o Experimental tests and theory predictions: gravitational bending of light, precession of mercury’s orbit, gravitational slowing of time and gravitational red shift, gravitational waves. • Understand the effects on clocks of a very large mass. - An observer will note a slowing of clocks (time dilation) and a shortening of rulers (length contraction) that are moving with respect to the observer - This effect becomes significant only if the clock or ruler is moving at a substantial fraction of the speed of light • How and where do black holes form? - Formation in binary systems: 1 A Type II supernova with a stellar corpse M > 3 MSun, this core goes gravitational collapse to form a black hole. 2 A white dwarf or a neutron star accretes enough matter from its companion star. 3 Two dead stars coalescing to form a black holes (like two neutron stars orbiting each other, lose energy and crash). • Understand how we know of a black hole's existence. - These are detected by observing the motions of material around the black hole (searching for the radiation emitted by material as it falls into a hole) • Understand the concepts of singularity, event horizon and Schwarzchild Radius. - The entire mass of a black hole is concentrated in an infinitely dense singularity
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- The singularity is surrounded by a surface called the event horizon, where the escape speed equals the speed of light - Nothing—not even light—can escape from inside the event horizon - R Sch =2GM/c 2 Schwarzschild radius • Black holes physical properties. -
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This note was uploaded on 04/28/2010 for the course ASTR 113 taught by Professor Geller during the Spring '08 term at George Mason.

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EXAM 3 Study Guide - Relativity and Black Holes Understand...

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