Titlebook: Differential Geometry and General Relativity; Volume 1 Canbin Liang,Bin Zhou Textbook 2023 Science Press 2023 Differential Manifold.Tensor

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Lie Derivatives, Killing Fields and Hypersurfaces,Suppose . and . are manifolds (whose dimensions can be different) and . is a smooth map. Let . and . represent the collection of all smooth tensor fields of type (.,?.) on . and ., respectively. . naturally induces a series of maps as follows.

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Differential Forms and Their Integrals,We first introduce “forms” on an .-dimensional vector space ., and then discuss “differential forms” on an .-dimensional manifold ..

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,Solving Einstein’s Equation,Solving Einstein’s Equation is an important problem in general relativity. Many exact solutions play important roles in the study and development of general relativity. Since Einstein’s equation is a highly nonlinear partial differential equation, finding an (exact) solution in the general case is rather difficult.

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Special Relativity,nd time are treated separately in specific coordinate systems. However, after acquiring an understanding of differential geometry in the previous chapters, one can also use a 4-dimensional “global” way to formulate special relativity, which not only makes it easier to grasp the essence of the theory

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Schwarzschild Spacetimes,sed mainly on finding the solution. In view of the essentialness of the Schwarzschild solution, this chapter will further discuss several intimately related problems: Sect.?. discusses the timelike and null geodesics in Schwarzschild spacetime; Sect.?. introduces three experimental tests of general

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Cosmology I,out, and drawn conclusions concerning the universe. However, it is only after the development of general relativity that cosmology became a genuine science. From the point of view of general relativity, the universe?is the maximal spacetime containing everything in Nature, with its curvature on larg

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1868-4513 rs at various levels.Uses pedagogic features including numer.This book, the first in a three-volume set, explains general relativity using the mathematical tool of differential geometry. The book consists of ten chapters, the first five of which introduce differential geometry, which is widely appli