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chapter15 - CHAPTER 15 General Relativity 15.1 15.2 15.3...

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    15.1 Tenets of General Relativity 15.2 Tests of General Relativity 15.3 Gravitational Waves 15.4 Black Holes 15.5 Frame Dragging CHAPTER 15 General Relativity General Relativity There is nothing in the world except empty, curved space. Matter, charge, electromagnetism, and other fields are only manifestations of the curvature. - John Archibald Wheeler Albert Einstein (1879-1955) An excellent introductory General Relativity text
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    Inertial Mass and Gravitational Mass Recall from Newton’s 2 nd Law that an object accelerates in reaction to a force according to its inertial mass , m i : Inertial mass measures how strongly an object resists a change in its motion. Gravitational mass , m g , measures how strongly it attracts and is attracted by other objects: Equating the forces, we get a ratio of masses: We always take the inertial and gravitational masses to be equal. Einstein considered this equivalence fundamental. 2 g g GMm F m g r = = i F m a = 2 GM g r = where: g i m a g m =
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    15.1: Tenets of General Relativity General relativity is the extension of special relativity to non-inertial (accelerating) frames. And because the effects of gravity and acceleration prove to be indistinguishable, it will also be a theory of gravity. It’s based on two concepts: (1) the principle of equivalence—the extension of Einstein’s first postulate of special relativity to the case of non-inertial reference frames. (2) the modeling of these effects as the curvature of space- time due to matter.
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    Principle of Equivalence The principle of equivalence is an experiment in non-inertial reference frames. Consider an astronaut sitting in a confined space on a rocket placed on Earth. The astronaut sits on a scale that indicates a mass M . The astronaut also drops a safety manual that falls to the floor. Next, we’ll ask what happens when the rocket takes off and accelerates through empty space.
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    Principle of Equivalence Now let the rocket accelerate through space, where grav- ity is negligible. If the acceleration is g , then the scale indicates the same mass M that it did on Earth, and the safety manual still falls with the same acceleration as measured on earth. The question is: How can the astronaut tell whether the rocket is at rest on earth or accelerating in space? Principle of equivalence : There is no experiment that can be done in a small confined space that can detect the difference between a uniform gravitational field and an equivalent uniform acceleration.
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    Light Deflection Consider accelerating where gravity is negligible, with a window to allow a beam of starlight to enter the spacecraft. Since the velocity of light is finite, it takes time for the light to reach the spaceship’s opposite wall. During this time, the rocket has accelerated upward.
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