General Relativity and Cosmology for Undergraduates

By Norbury, John W., Professor

Book Id: WPLBN0000659719
Format Type: PDF eBook
File Size: 675.43 KB.
Reproduction Date: 2005

Title:	General Relativity and Cosmology for Undergraduates
Author:	Norbury, John W., Professor
Volume:
Language:	English
Subject:	Science., Physics, Physics--Research
Collections:	Physics Literature
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Citation APA MLA Chicago W. Norbur, P. J. (n.d.). General Relativity and Cosmology for Undergraduates. Retrieved from http://gutenberg.cc/

Description
Physics Literature

Excerpt
Introduction: Many of the modern ideas in cosmology can be explained without the need to discuss General Relativity. The present chapter represents an attempt to do this based entirely on Newtonian mechanics. The equations describing the velocity (called the Friedmann equation) and acceleration of the universe are derived from Newtonian mechanics and also the cosmological constant is introduced within a Newtonian framework. The equations of state are also derived in a very simple way. Applications such as conservation laws, the age of the universe and the radiation and matter dominated epochs are discussed.

Table of Contents
Contents 1 NEWTONIAN COSMOLOGY 5 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Velocity and Acceleration Equations . . . . . . . . . . . . . . 7 1.4 Cosmological Constant . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 Einstein Static Universe . . . . . . . . . . . . . . . . . 11 2 APPLICATIONS 13 2.1 Conservation laws . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Inøation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Quantum Cosmology . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.1 Derivation of the SchrŽodinger equation . . . . . . . . . 16 2.4.2 Wheeler-DeWitt equation . . . . . . . . . . . . . . . . 17 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.8 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 TENSORS 23 3.1 Contravariant and Covariant Vectors . . . . . . . . . . . . . . 23 3.2 Higher Rank Tensors . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Review of Cartesian Tensors . . . . . . . . . . . . . . . . . . . 27 3.4 Metric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.1 Special Relativity . . . . . . . . . . . . . . . . . . . . . 30 3.5 Christo?el Symbols . . . . . . . . . . . . . . . . . . . . . . . . 31