By Thomas A. Moore
A common Relativity Workbook is a textbook meant to help a one-semester undergraduate path on normal relativity. via its specific workbook-based layout, it allows scholars to increase a high-quality mastery of either the physics and the assisting tensor calculus through guiding them to paintings throughout the implications. the math is brought steadily and in a totally actual context. every one bankruptcy, that's designed to correspond to at least one type consultation, contains a brief assessment of the thoughts with no obscuring derivations or info, via a sequence of packing containers that advisor scholars during the means of operating issues out. This active-learning process allows scholars to increase a safer mastery of the fabric than extra conventional ways. greater than 350 homework difficulties aid additional studying.
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Extra resources for A general relativity workbook
11 still describes the relationship ∆t´ in the clock frame ∆t in the ground frame. 6 Imagine that a train is moving at a speed of 4/5. 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 .
It is also conventional to define the object’s relativistic momentum p to be the 3-dimensional vector whose components are the spatial components of p, and p 2 = (p x) 2 + (p y) 2 + (p z) 2 as the squared magnitude of p (the notation p 2 distinguishes it from p2 / p : p ). 16) E is called the object’s relativistic energy not only because it is conserved (along with the other components of p) but because when v << 1, m2 = E2 - p 2 and E . 3 ). We see that at such velocities, an object’s conserved relativistic energy E reduces to its newtonian kinetic energy plus a term equal to its mass.
We will see why this is crucial shortly, but for now, note that this at least treats all the spacetime coordinates symmetrically, and that the object’s proper time x is a frame-independent parameter, so all observers agree about its value at a given event along the object’s worldline. 1: A spacetime diagram displaying an object’s worldline. We can label events along the worldline according to the proper time x measured by the object from some suitable starting event. An object’s four-velocity u is tangent to the worldline at each event and inside the event’s light cone.