Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes
General relativity is the modern theory of the gravitational field. It is a deep subject that couples—fluid dynamics to the geometry of spacetime through the Einstein equations. The subject has seen a resurgence of interest recently, partlybecauseof thespectacularsatellitedatathatcontinuestoshednewlight on the nature of the universe. . . Einstein’s theory of gravity is still the basic theorywehavetodescribetheexpandinguniverseofgalaxies. ButtheEinstein equations are of great physical, mathematical and intellectual interest in their own right. They are the granddaddy of all modern field equations, being the first to describe a field by curvature, an idea that has impacted all of physics, and that revolutionized the modern theory of elementary particles. In these noteswedescribeamathematicaltheoryofshockwavepropagationingeneral relativity. Shock waves are strong fronts that propagate in—fluids, and across which there is a rapid change in density, pressure and velocity, and they can bedescribedmathematicallybydiscontinuitiesacrosswhichmass,momentum and energy are conserved. In general relativity, shock waves carry with them a discontinuity in spacetime curvature. The main object of these notes is to introduce and analyze a practical method for numerically computing shock waves in spherically symmetric spacetimes. The method is locally inertial in thesensethatthecurvatureissetequaltozeroineachlocalgridcell. Although it formally appears that the method introduces singularities at shocks, the arguments demonstrate that this is not the case. The third author would like to dedicate these notes to his father, Paul Blake Temple, who piqued the author’s interest in Einstein’s theory when he was a young boy, and whose interest and encouragement has been an inspirationthroughout his adult life.
1103818248
Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes
General relativity is the modern theory of the gravitational field. It is a deep subject that couples—fluid dynamics to the geometry of spacetime through the Einstein equations. The subject has seen a resurgence of interest recently, partlybecauseof thespectacularsatellitedatathatcontinuestoshednewlight on the nature of the universe. . . Einstein’s theory of gravity is still the basic theorywehavetodescribetheexpandinguniverseofgalaxies. ButtheEinstein equations are of great physical, mathematical and intellectual interest in their own right. They are the granddaddy of all modern field equations, being the first to describe a field by curvature, an idea that has impacted all of physics, and that revolutionized the modern theory of elementary particles. In these noteswedescribeamathematicaltheoryofshockwavepropagationingeneral relativity. Shock waves are strong fronts that propagate in—fluids, and across which there is a rapid change in density, pressure and velocity, and they can bedescribedmathematicallybydiscontinuitiesacrosswhichmass,momentum and energy are conserved. In general relativity, shock waves carry with them a discontinuity in spacetime curvature. The main object of these notes is to introduce and analyze a practical method for numerically computing shock waves in spherically symmetric spacetimes. The method is locally inertial in thesensethatthecurvatureissetequaltozeroineachlocalgridcell. Although it formally appears that the method introduces singularities at shocks, the arguments demonstrate that this is not the case. The third author would like to dedicate these notes to his father, Paul Blake Temple, who piqued the author’s interest in Einstein’s theory when he was a young boy, and whose interest and encouragement has been an inspirationthroughout his adult life.
54.99
In Stock
5
1
Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes
152
Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes
152
54.99
In Stock
Product Details
| ISBN-13: | 9780387350738 |
|---|---|
| Publisher: | Springer New York |
| Publication date: | 11/30/2006 |
| Series: | Springer Monographs in Mathematics |
| Edition description: | 2007 |
| Pages: | 152 |
| Product dimensions: | 6.10(w) x 9.25(h) x 0.02(d) |
From the B&N Reads Blog