2003/07/31 by A. Das, Andrew DeBenedictis, A. DeBenedictis +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1063/1.1621056
published as J.Math.Phys. 44 (2003) 5637-5655 · 23 pages, 1 figure, uses AMS packages. Updated version has corrected typos as well as added comments and extension regarding ISLD junction conditions. Accepted for publication in Journal of Mathematical Physics
arxiv created 2003/09/10 · openalex publication_date 2003/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Einstein’s spherically symmetric interior gravitational equations are investigated. Following Synge’s procedure, the most general solution of the equations is furnished in case T11 and T44 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 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.