A general relativity workbook by Thomas A. Moore

By Thomas A. Moore

A common Relativity Workbook is a textbook meant to aid a one-semester undergraduate path on common relativity. via its designated workbook-based layout, it permits scholars to strengthen a superior mastery of either the physics and the aiding tensor calculus by way of guiding them to paintings in the course of the implications. the maths is brought steadily and in a totally actual context. every one bankruptcy, that is designed to correspond to 1 type consultation, includes a quick evaluate of the innovations with no obscuring derivations or information, via a chain of containers that consultant scholars during the means of operating issues out. This active-learning process allows scholars to advance a safer mastery of the cloth than extra conventional techniques. greater than 350 homework difficulties help additional studying.

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A passenger points a laser out the train window perpendicular to the tracks, and the laser emits a brief flash of light. What angle does the velocity of this light flash make with the tracks in the ground frame? 3 Four-Vectors Introduction Flat Spacetime • Review of Special Relativity • Four-Vectors • Index Notation Tensors • Arbitrary Coordinates • Tensor Equations • Maxwell’s Equations • Geodesics The Calculus of Curvature • The Absolute Gradient • Geodesic Deviation • The Riemann Tensor The Einstein Equation • The Stress-Energy Tensor • The Einstein Equation • Interpreting the Equation • The Schwarzschild Solution Cosmology • The Universe Observed • A Metric for the Cosmos • Evolution of the Universe • Cosmic Implications • The Early Universe • CMB Fluctuations & Inflation Gravitational Waves • Gauge Freedom • Detecting Gravitational Waves • Gravitational Wave Energy • Generating Gravitational Waves • Gravitational Wave Astronomy Schwarzschild Black Holes • The Schwarzschild Metric • Particle Orbits • Precession of the Perihelion • Photon Orbits • Deflection of Light • Event Horizon • Alternative Coordinates • Black Hole Thermodynamics Spinning Black Holes • Gravitomagnetism • The Kerr Metric • Kerr Particle Orbits • Ergoregion and Horizon • Negative-Energy Orbits 26 3 Four-Vectors t Describing Motion in Terms of Proper Time .

1 . 25. 4 Conservation of Momentum or Four-momentum? BEFORE m v (a) m m v AFTER M BEFORE v1lx = 0, m 2v 1 + v2 (b) A single counterexample suffices to show that conservation of newtonian momentum is inconsistent with the principle of relativity. Consider the following collision as an example. 3a). Let us define coordinates so that v1 points in the +x direction. The particles then collide and form a single particle at rest with mass M= 2m. The total newtonian momentum of this system is clearly zero before and after the collision and so it is conserved in frame S.

But this is absurd. 4b) the rails! Our original assumption must therefore be false: observers in two IRFs must in fact agree about the values of distances measured perpendicular to the line of relative motion. ) For two frames in standard orientation, then we must have y´ = y and z´ = z if the principle of relativity holds. Comparing coordinate times . Now we will show that a clock at rest in S´ that is present at two events registers their time coordinate difference to be Tt l = Tt 1 - b2 , where ∆t is the coordinate time difference between those same events as registered by a pair of synchronized clocks in frame S.

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