Global Aspects in Gravitation and Cosmology (International by Pankaj S. Joshi

By Pankaj S. Joshi

This ebook describes worldwide elements in gravitation concept and cosmology in the framework of Einstein's concept of gravity. subject matters comprise effects at the constitution and topology of space-time, particular recommendations to Einstein equations and singularities, the prestige of quantum gravity, and quantum results close to space-time singularities in robust curvature fields. the writer additionally discusses the character and constitution of space-time singularities, the cosmic censorship challenge in black gap physics, and the difficulty of quantum results in powerful gravity fields. scholars and mathematicians, astrophysicists, and physicists will locate this theoretically wealthy publication a landmark in relativity theory.

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Extra resources for Global Aspects in Gravitation and Cosmology (International Series of Monographs on Physics)

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Wr, Xi, ... , X s) = T (w 1 , ... , wr, Xi , . . , X s) + T'(w 1, ... ,wr, X1 , .. , Xs) , and the multiplication by a real number a is defined by 24 The manifold model far space-time The operation of outer product on two tensors T and T' of type (r, s) and (r', s') could now be defined in terms of their components to give a new tensor T © T' given by, This offers a way of constructing new tensors out of the vectors and dual vectors. A tensor field of (r, s) type on M is an assignment of a tensor of the same type at ali p in M.

E;,. @eh@ ... @el • } , forms a basis for the tensor prod uct r;· (p) with ali t he indices runni ng from 1 to n. Then, any tensor T E can b e expresscd as r; T -_ yii- .. ir . ei,. VY K>. K>. K>. K>. Js · · · '.

L . k . l =V + (\lk\l1T1)T) + R 1 k1iT V'T = Vk(\l k(Ti\liTJ)) + Rj ktiTkViT 1 = (Vk\lkTi)(\liTj) k . 102) = Rj ktiTkViTl. 103) is called the Jacobi equation or the equation of geodesic deviation. It is clear from the above that D 2 VJ = O if and only if all the components of the Riemann tensor are vanishing. On the other hand , whenever sorne components of the same are non-zero, then the neighbouring non-spacelike geodesics will necessarily accelerate towards or away from each other. 8 Einstein equations We discuss in this section the Einstein equations on a space-time manifold.

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