General solutions of Einstein's spherically symmetric gravitational equations with junction conditions

Details General solutions of Einstein's spherically symmetric gravitational equations with junction conditions General solutions of Einstein's spherically symmetric gravitational equations with junction conditions

2003-07-03

arxiv.org/abs/gr-qc/0307009v2

J.Math.Phys. 44 (2003) 5637-5655

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, 1 figure, uses AMS packages. Updated version has corrected typos as well as added comments and extension regarding I

Scientific paper

10.1063/1.1621056

Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a total mass function, $M(r,t)$, is rigorously proved. Under suitable restrictions on the total mass function, the Schwarzschild mass $M(r,t)=m$, implicitly defines the boundary of the spherical body as $r=B(t)$. Both Synge's junction conditions as well as the continuity of the second fundamental form are examined and solved in a general manner. The weak energy conditions for an \emph{arbitrary boost} are also considered. The most general solution of the spherically symmetric anisotropic fluid model satisfying both junction conditions is furnished. In the final section, various exotic solutions are explored using the developed scheme including gravitational instantons, interior $T$-domains and $D$-dimensional generalizations.

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