General Relativity

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Exploring Black Holes

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Exploring Black Holes
Introduction to General Relativity

Edwin F. Taylor and
John Archibald Wheeler

Addison Wesley Longman

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Albert Einstein told us that a star or other massive object distorts spacetime in its vicinity. Sufficient distortion makes it impossible to describe matter and motion with the single "inertial reference frame" used in Newton's theory of mechanics and Einstein's theory of special relativity. General relativity describes the distortion of spacetime near a star, white dwarf, neutron star, or black hole and predicts the resulting motion of stones, satellites, and light flashes.

Learning general relativity usually requires mastering Einstein's field equations, which are expressed in the complicated mathematics of tensors or differential forms. But big chunks of general relativity require only calculus if one starts with the metric describing spacetime around Earth or black hole. Expressions for energy and angular momentum follow, along with predictions for the motions of particles and light. Students study the Global Positioning system, precession of Mercury's orbit, gravitational red shift, orbits of light and deflection of light by Sun, frame-dragging and precession near a rotating body, gravitational waves, and two different models of the Universe.

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Software for plotting general-relativistic (and Newtonian) orbits plus student exercises are available for download at this website.