Mathematics – Logic
Scientific paper
Jun 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aipc..668..204d&link_type=abstract
COSMOLOGY AND GRAVITATION: Xth Brazilian School of Cosmology and Gravitation; 25th Anniversary (1977-2002). AIP Conference Proc
Mathematics
Logic
Mathematical And Relativistic Aspects Of Cosmology, Observational Cosmology, Classical General Relativity
Scientific paper
In the spherically symmetric case the dominant energy condition, together with the requirement of regularity of a density and finiteness of the mass, defines the family of asymptotically flat globally regular solutions to the Einstein minimally coupled equations which includes the class of metrics asymptotically de Sitter as r --> 0 and asymptotically Schwarzschild as r --> ∞. A source term connects smoothly de Sitter vacuum in the origin with the Minkowski vacuum at infinity and corresponds to anisotropic vacuum defined macroscopically by the algebraic structure of its stress-energy tensor invariant under boosts in the radial direction. Dependently on parameters, geometry describes vacuum nonsingular black and white holes, and self-gravitating particle-like structures. ADM mass for this class is related to both de Sitter vacuum trapped inside an object and to breaking of space-time symmetry. This class of metrics is easily extended to the case of nonzero cosmological constant at infinity. The source term connects then smoothly two de Sitter vacua and corresponds to extension of the Einstein cosmological term Λgμν to an r-dependent cosmological term Λμν. In this approach a constant scalar Λ associated with a vacuum density Λ = 8πGρvac, becomes a tensor component Λtt associated explicitly with a density component of a perfect fluid tensor whose vacuum properties follow from its symmetry and whose variability follows from the Bianchi identities. In this review we outline and discuss Λμν geometry and its applications.
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