Shock-wave solutions of the Einstein equations with perfect fluid sources : existence and consistency by a locally inertial Glimm scheme / Jeff Groah, Blake Temple.

Format:

Book

Author/Creator:

Groah, Jeff, author.

Temple, Blake, author.

Series:

Memoirs of the American Mathematical Society ; Volume 172, Number 813.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 172, Number 813

Language:

English

Subjects (All):

Conservation laws (Physics).

Einstein field equations.

Shock waves.

Singularities (Mathematics).

General relativity (Physics).

Physical Description:

1 online resource (98 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2004.

Language Note:

English

Summary:

Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.

Contents:

""Contents""; ""1 Introduction""; ""1.1 The Proof Strategy""; ""1.2 A Locally Inertial Glimm Scheme""; ""1.3 The Smoothness Class of the Metric""; ""2 Preliminaries""; ""3 The Fractional Step Scheme""; ""4 The Riemann Problem Step""; ""5 The ODE Step""; ""6 Estimates for the ODE step""; ""7 Analysis of the Approximate Solutions""; ""8 The Elimination of Assumptions""; ""9 Convergence""

Notes:

"Volume 172, Number 813 (second of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0414-1