Generating static spherically symmetric anisotropic solutions of Einstein's equations from isotropic Newtonian solutions

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 80, Issue 6, 2009, Pages

  Lake, Kayll ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349876387     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.80.064039     Document Type: Article

References (37)

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10. For further solutions, see, for example, J. Loranger and K. Lake, Phys. Rev. D PRVDAQ 1550-7998 78, 127501 (2008); 10.1103/PhysRevD.78.127501
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28. S. Chandrasekhar, An Introduction to the Study of Stellar Structure (University of Chicago Press, Chicago, 1939).
29. In the present notation, the weak energy condition requires ρ0, ρ+P0 and ρ+p0; the strong energy condition requires ρ+P0, ρ+p0 and ρ+2P+p0; and the dominant energy condition requires ρ0, ρ|P| and ρ|p|. See, for example, M. Visser, Lorentzian Wormholes (Springer-Verlag, New York, 1996);
30. E. Poisson, A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge University Press, Cambridge, England, 2004).
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34. The resultant bounds on the surface redshift are given by B.V. Ivanov, Phys. Rev. D PRVDAQ 0556-2821 65, 104011 (2002). 10.1103/PhysRevD.65.104011
35. It is important to note that the solution we are considering is not the most general solution to 4 with constant ρ. Rather, it is the solution, with constant ρ, that satisfies 8. Compare, for example, R.L. Bowers and E.P.T. Liang, Astrophys. J. 188, 657 (1974). ASJOAB 0004-637X 10.1086/152760
36. A proof by S.A. Levin can be found at http://sepwww.stanford.edu/oldsep/ stew/descartes.pdf.
37. This is a package which runs within Maple. It is entirely distinct from packages distributed with Maple and must be obtained independently. The GRTensorII software and documentation are distributed freely on the World Wide Web from the address http://grtensor.org.