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

Consensus

货物

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.

GRILL

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

euphoria

,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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obscurity

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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certitude

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