The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
A mathematical function is said to be singular at a point if it "blows up" there; that is, if the function evaluated at that point becomes infinite. The point is a singularity of that particular function.
In physics, any point at which the mathematical expression for a physical quantity becomes infinite is a singular point. Thus, for example, the origin, r=0 is a singularity of the Coulomb expression for the electric field surrounding a point charge, q, given by E=kq/r[sup2 ].
When discussing the physics of space-time, the relevant mathematical function is the curvature, which is represented mathematically by the Riemann curvature tensor. The Riemann tensor has twenty independent components, each of which is a function of the space-time coordinates. Loosely speaking, a space-time point at which any component of the Riemann tensor blows up is called a singular point, or a singularity. There is a curvature singularity in the Schwarzchild space-time geometry, again at the origin, r=0. As physical quantities can never take on infinite values, the laws of physics break down at a singularity--they lose their power to predict the results of a physical measurement.
This is referred to as "loosely speaking" because it is quite hard (and perhaps impossible) to give meaning to the idea of a singularity as a "place" in space-time if the very concept of space-time breaks down. The rigorous mathematical definition is thus more complicated, but in this, as in many other things, the simple, more intuitive picture certainly suffices as a way of visualization.