# An Introduction to Relativity by Jayant V. Narlikar

By Jayant V. Narlikar

Common relativity is now a vital a part of undergraduate and graduate classes in physics, astrophysics and utilized arithmetic. this straightforward, easy advent to relativity is perfect for a primary direction within the topic. starting with a finished yet basic evaluation of distinctive relativity, the e-book creates a framework from which to release the guidelines of normal relativity. After describing the fundamental concept, it strikes directly to describe vital functions to astrophysics, black gap physics, and cosmology. numerous labored examples, and diverse figures and photographs, aid scholars relish the underlying ideas. There also are one hundred eighty routines which attempt and increase students' knowing of the topic. The textbook provides all of the important details and dialogue for an common method of relativity. Password-protected ideas to the routines can be found to teachers at www.cambridge.org/9780521735612.

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4 illustrates the situation. Let a vector A be shown by arrow OP. How do we specify the two components of this vector? There are two obvious ways. One is to draw straight lines through P parallel to the axes intersecting them at R1 and R2 , respectively. The lengths OR1 and OR2 then specify nt 48 Vectors and tensors Fig. 4. If the axes are not rectangular, even in Euclid’s geometry the covariant and contravariant components of a vector are different, as seen here. ) X2 S2 R2 P x2 β X1 O x1 R1 S1 the contravariant components of the vector.

Show that mω mω = √ . B= √ 2 q 1−v q 1 − ω2 R 2 9. A source of light is moving towards an observer with speed v such that its direction of motion makes an angle θ with the line of sight to the source. If there is zero Doppler shift, find θ . 10. From the observation formula derived in the text show that a source viewed from the Earth today and six months later will show a shift in direction equal to 2v/c × sin θ , where θ is the angle the direction to the source makes with the Earth’s motion. Estimate the order of magnitude of the effect.

It cannot be ‘turned on’ or ‘turned off ’. So we should not talk of the dotted trajectory, dealing as it does with a possibility that cannot happen. The continuous trajectory is the only trajectory that we have to interpret. Only we now assume that the geometry of spacetime in which the stone is moving is non-Euclidean, being rendered so by the presence of Earth’s gravity. So the apparently paraboliclooking trajectory is actually describing ‘straight line motion with a uniform velocity’ but in a non-Euclidean spacetime.