A Relativist’s Toolkit : The Mathematics Of Black-hole Mechanics

Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83091-1 - A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Frontmatter More information © Cambridge University Press www.cambridge.org 1 Fundamentals This first chapter is devoted to a brisk review of the fundamentals of differential geometry. The collection of topics presented here is fairly standard, and most of these topics should have been encountered in a previous introductory course on general relativity. Some, however, may be new, or may be treated here from a different point of view, or with an increased degree of completeness. We begin in Section 1.1 by providing definitions for tensors on a differentiable manifold. The point of view adopted here, and throughout the text, is entirely unsophisticated: We do without the abstract formulation of differential geometry and define tensors in the old-fashioned way, in terms of how their components transform under