All static spherically symmetric anisotropic solutions of Einstein’s equations

2007/12/31 by L. Herrera, J. Ospino, A. Di Prisco · 10 citations
Mathematics · Physics and Astronomy · #Anisotropy #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Einstein equations #Einstein field equations #Formalism (music) #General relativity #Mathematical analysis #Mathematics #Perfect fluid #Physics #Quantum mechanics #Relativity and Gravitational Theory #SPHERES #Theoretical physics #astro-ph #gr-qc

paper · pdf · doi:10.1103/physrevd.77.027502

published as Phys.Rev.D77:027502,2008 · 8 pages Latex. To appear in Phys. Rev. D. New reference added. Some references corrected

arxiv created 2008/01/15 · openalex publication_date 2008/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the knowledge of two functions (instead of one) to generate all possible solutions. To illustrate the method some known cases are recovered.

Citations

• Local anisotropy in self-gravitating systems
• Gravastar solutions with continuous pressures and equation of state
• On Einstein clusters as galactic dark matter haloes

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