American Journal of Physics and Applications
Volume 4, Issue 2, March 2016, Pages: 50-56
Received: Mar. 24, 2016;
Published: Mar. 25, 2016
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Napasorn Jongjittanon, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Petarpa Boonserm, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Tritos Ngampitipan, Faculty of Science, Chandrakasem Rajabhat University, Bangkok, Thailand
For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.
Generating Theorems for Charged Anisotropy in General Relativity, American Journal of Physics and Applications.
Vol. 4, No. 2,
2016, pp. 50-56.
K. Schwarzschild, “On the gravitational field of a sphere of incompressible fluid according to Einstein’s theory”, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1916 (1916) 424 [arXiv: physics/9912033 [physics. hist-ph]].
P. Boonserm, M. Visser and S. Weinfurtner, “Generating perfect fluid spheres in general relativity”, Phys. Rev. D 71 (2005) 124037 [arXiv: gr-qc/0503007].
S. Carroll, “Spacetime and geometry: an introduction to general relativity”, Pearson new international edition, U.S.A., Pearson Education Limited, 2014.
H. Bondi, “Spherically symmetrical models in general relativity”, Mon. Not. Roy. Astron. Soc. 107 (1947) 410.
H. A. Buchdahl, “General relativistic fluid spheres”, Phys. Rev. 116 (1959) 1027-1034.
M. S. R. Delgaty and K. Lake, “Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations”, Compute. Phys. Commun. 115 (1998) 395 [arXiv: gr-qc/9809013].
P. Boonserm, M. Visser and S. Weinfurtner, “Solution generating theorems for the TOV equation”, Phys. Rev. D 76 (2007) 044024 [arXiv: gr-qc/0607001].
A. Sulaksono, “Anisotropic pressure and hyperon in neutron stars,” Int. J. Mod. Phys. E 24 (2015) 01, 1550007 [arXiv: 1412.7274 [nucl-tn]].
P. Boonserm, T. Ngampitipan and M. Visser, “Mimicking static anisotropic fluid spheres in general relativity”, International Journal of Modern Physics D (2015): 1650019 [arXiv: 1501.07044v3 [gr-qc]].
P. Boonserm, “Some exact solution in general relativity”, MSc. Thesis, Victoria University of Wellington, 2006.
Chandrasekhar, S. (1998). The Mathematical Theory of Black Holes (Reprinted ed.). Oxford University Press. p. 205. ISBN 0-19850370-9. Retrieved 13 May 2013.
K. Komathiraj ans S. D. Maharaj, “A class of charged relativistic spheres”, Mathematical and Computational Applications 15, 665-673, 2010.
Patel, L. K., and N. P. Mehta. "An exact model of an anisotropic relativistic sphere." Australian Journal of Physics 48.4 (1995): 635-644.
Ray, Saibal, and Basanti Das, “Tolman-Bayin type static charged fluid spheres in general relativity.” Monthly Notices of the Royal Astronomical Society 349.4 (2004), 1331-1334.
K. Thairatana, “Transformation for perfect fluid spheres in isotropic coordinates”, MSc. Thesis, Chulalongkorn University, 2013.
K. Lake, “all static spherically symmetric perfect fluid solutions of Einstein’s equation”, Phys. Rev. D 67 (2003) 104015 [gr-qc/0209104].
S. Rahman and M. Visser, “Space-time geometry of static fluid spheres”, Class. Quant. Grav. 19 (2002) 935 [gr-qc/0103065].
S. S. Bayin, “Anisotropic fluid spheres in general relativity”, Phys. Rev. D 26 (1982) 1262.
L. Herrera, J. Ospino and A. Di Prisco, “All static spherically symmetric anisotropic solutions of Einstein’s equation”, Phys. Rev. D 77 (2008) 027502 [arXiv: 0712.0713 [gr-qc]].