Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes

1999/03/02 by K. Anguige, K.P. Tod, K. P. Tod · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #gr-qc

paper · pdf · doi:10.1006/aphy.1999.5946

published as Annals Phys. 276 (1999) 257-293 · LaTeX, 43 pages, no figures, submitted to Ann. Phys

arxiv created 1999/03/02 · arxiv updated 2009/11/30

Abstract

We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy problem for these equations is well-posed, that is to say that solutions exist, are unique and depend smoothly on the data, with data consisting of simply the 3-metric of the singularity. The analogous result for gamma=1 (dust) is obtained when Bianchi type symmetry is assumed.

Cited by

• A global conformal extension theorem for perfect fluid Bianchi space-times
• Isotropic cosmological singularities in spatially homogeneous models with a cosmological constant
• Local and Global Existence Theorems for the Einstein Equations. [europepmc]
• Theorems on Existence and Global Dynamics for the Einstein Equations. [europepmc]
• Theorems on Existence and Global Dynamics for the Einstein Equations. [europepmc]
• Conformal methods in mathematical cosmology. [europepmc]