By James Foster, J. David Nightingale

ISBN-10: 0387260781

ISBN-13: 9780387260785

ISBN-10: 0387275835

ISBN-13: 9780387275833

This textbook offers an outstanding advent to a subject that's tremendous effortless to get slowed down in. I took a one semester path that used this article as an undergraduate, in which i assumed the ebook was once in simple terms respectable, yet then while I took a gradute path that used Carroll's Spacetime and Geometry is whilst i actually got here to understand the guidance this e-book gave me (not that Carroll's booklet is undesirable, I simply would not suggest it for a primary reading). let alone the booklet is beautiful reasonable so far as physics texts pass.

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**Example text**

2. 6 shows the torus generated by revolving the circle (x-a)2+ z2 = b2 (where a> b > 0) in the plane y = 0 about the z axis. Show that when the angles Band ¢ are used as parameters (see figure) points on the torus are given by x=(a+bcosB)cos¢, y=(a+bcosB)sin¢, z=bsinB, 50 1 Vector and tensor fields z Generating circle with center at (a, 0, 0) and radius b y x Fig. 6. The torus generated by revolving a circle about the z axis. e with - 7f < ~ 7f and - 7f < ¢ ~ tt . Obtain expressions for th e natural basis vectors eo and eet> , and hence obtain the metric tensor components g AB.

83) (often written without the modulus signs, even in th e indefinite case), and defines the line element of the manifold M . 1, v = 0,1 ,2,3) has an indefiniteness characterized by (+ - --) . v = 0 . { spacelike <0 These descriptions are also applied to curves. If the tangent vectors to a curve (or part of a curve) are timelike, we describe the curve (or part of the cur ve) as timelike, and extend the descriptions null and spacelike in a similar way. We shall see in the next chapter, where our model for spacetime is more fully developed, that a particle with mass follows a timelike path, while a photon follows a null path.

We now consider some operations with tensors. Th e first of these is addition: adding corresponding components of two tensors of th e same type results in quantities that are th e components of a tensor of that type. The second is multiplication by scalars: multiplying each component of a tensor by a scalar quantity results in quantities that are th e components of a tensor of the same type . The validity of th ese two operations is clear from the transformation formula for components. The third operation is tensor multiplication which gives the tensor product of two tensors.

### A Short Course in General Relativity by James Foster, J. David Nightingale

by James

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