Well Behaved Parametric Class of Exact Solutions of Einstein-Maxwell Field Equations in General Relativity

ABSTRACT

We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ_{b} = 2 × 10^{14}g/cm^{3}. Corresponding to K = 0.72 with X = 0.15, the resulting well behaved model has the mass M = 1.94 MΘ with radius r_{b} » 15.2 km and for K = 2.41 with X = 0.15, the resulting well behaved model has the mass M = 2.26 MΘ with radius r_{b} » 14.65 km.

We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ

Cite this paper

nullN. Pant, B. Tewari and P. Fuloria, "Well Behaved Parametric Class of Exact Solutions of Einstein-Maxwell Field Equations in General Relativity,"*Journal of Modern Physics*, Vol. 2 No. 12, 2011, pp. 1538-1543. doi: 10.4236/jmp.2011.212186.

nullN. Pant, B. Tewari and P. Fuloria, "Well Behaved Parametric Class of Exact Solutions of Einstein-Maxwell Field Equations in General Relativity,"

References

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[2] W. B. Bonnor, “The Equilibrium of Charged Sphere,” Monthly Notices of the Royal Astronomical Society, Vol. 137, No. 3, 1965, pp. 239-251.

[3] M. S. R. Delgaty and K. Lake, “Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid So- lutions of Einstein’s Equations,” Computer Physics Com- munications, Vol. 115, No. 2-3, 1998, pp. 395-399. doi:10.1016/S0010-4655(98)00130-1

[4] N. Pant, “Some new Exact Solutions with Finite Central Parameters and Uniform Radial Motion of Sound,” As- trophysics and Space Science, Vol. 331, No. 2, 2011, pp. 633-644.

[5] N. Pant, et al., “New Class of Regular and Well Behaved Exact Solutions in General Relativity,” Astrophysics and Space Science, Vol. 330, No. 2, 2010, pp. 353-370. doi:10.1007/s10509-010-0383-1

[6] N. Pant, et al., “Well Behaved Class of Charge Analogue of Heintzmann’s Relativistic Exact Solution,” Astrophys- ics and Space Science, Vol. 332, No. 2, 2011, pp. 473- 479. doi:10.1007/s10509-010-0509-5

[7] N. Pant, et al., “Variety of Well Behaved Parametric Classes of Relativistic Charged Fluid Spheres in General Relativity,” Astrophysics and Space Science, Vol. 333, No. 1, 2011, pp. 161-168. doi:10.1007/s10509-011-0607-z

[8] S. K. Maurya and Y. K. Gupta, “A Family of Well Behaved Charge Analogue of a Well Behaved Neutral Solu- tion in Genetral Relativity,” Astrophysics and Space Sci- ence, Vol. 332, No. 2, 2011, pp. 481-490. doi:10.1007/s10509-010-0541-5

[9] Y. K. Gupta and S. K. Maurya, “A Class of Regular and Well Behaved Relativistic Super Dense Star Models,” Astrophysics and Space Science, Vol. 334, No. 1, 2011, pp. 155-162. doi:10.1007/s10509-010-0503-y

[10] N. Pant, “Well Behaved Parametric Class of Relativistic in Charged Fluid Ball General Relativity,” Astrophysics and Space Science, Vol. 332, No. 2, 2011, pp. 403-408. doi:10.1007/s10509-010-0521-9

[11] M. J. Pant and B. C. Tewari, “Well Behaved Class of Charge Analogue of Adler’s Relativistic Exact Solution,” Journal of Modern Physics, Vol. 2, No. 6, 2011, pp. 481- 487. doi:10.4236/jmp.2011.26058

[12] R. J. Adler, “A Fluid Sphere in General Relativity,” Jour- nal of Mathematical Physics, Vol. 15, No. 6, 1974, pp. 727-729. doi:10.1063/1.1666717

[1] J. C. Graves and D. R. Brill, “Oscillatory Character of Reissner Nordstorm Metric for an Ideal Charged Wormhole,” Physical Review, Vol. 120, No. 4, 1960, pp. 1507- 1513. doi:10.1103/PhysRev.120.1507

[2] W. B. Bonnor, “The Equilibrium of Charged Sphere,” Monthly Notices of the Royal Astronomical Society, Vol. 137, No. 3, 1965, pp. 239-251.

[3] M. S. R. Delgaty and K. Lake, “Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid So- lutions of Einstein’s Equations,” Computer Physics Com- munications, Vol. 115, No. 2-3, 1998, pp. 395-399. doi:10.1016/S0010-4655(98)00130-1

[4] N. Pant, “Some new Exact Solutions with Finite Central Parameters and Uniform Radial Motion of Sound,” As- trophysics and Space Science, Vol. 331, No. 2, 2011, pp. 633-644.

[5] N. Pant, et al., “New Class of Regular and Well Behaved Exact Solutions in General Relativity,” Astrophysics and Space Science, Vol. 330, No. 2, 2010, pp. 353-370. doi:10.1007/s10509-010-0383-1

[6] N. Pant, et al., “Well Behaved Class of Charge Analogue of Heintzmann’s Relativistic Exact Solution,” Astrophys- ics and Space Science, Vol. 332, No. 2, 2011, pp. 473- 479. doi:10.1007/s10509-010-0509-5

[7] N. Pant, et al., “Variety of Well Behaved Parametric Classes of Relativistic Charged Fluid Spheres in General Relativity,” Astrophysics and Space Science, Vol. 333, No. 1, 2011, pp. 161-168. doi:10.1007/s10509-011-0607-z

[8] S. K. Maurya and Y. K. Gupta, “A Family of Well Behaved Charge Analogue of a Well Behaved Neutral Solu- tion in Genetral Relativity,” Astrophysics and Space Sci- ence, Vol. 332, No. 2, 2011, pp. 481-490. doi:10.1007/s10509-010-0541-5

[9] Y. K. Gupta and S. K. Maurya, “A Class of Regular and Well Behaved Relativistic Super Dense Star Models,” Astrophysics and Space Science, Vol. 334, No. 1, 2011, pp. 155-162. doi:10.1007/s10509-010-0503-y

[10] N. Pant, “Well Behaved Parametric Class of Relativistic in Charged Fluid Ball General Relativity,” Astrophysics and Space Science, Vol. 332, No. 2, 2011, pp. 403-408. doi:10.1007/s10509-010-0521-9

[11] M. J. Pant and B. C. Tewari, “Well Behaved Class of Charge Analogue of Adler’s Relativistic Exact Solution,” Journal of Modern Physics, Vol. 2, No. 6, 2011, pp. 481- 487. doi:10.4236/jmp.2011.26058

[12] R. J. Adler, “A Fluid Sphere in General Relativity,” Jour- nal of Mathematical Physics, Vol. 15, No. 6, 1974, pp. 727-729. doi:10.1063/1.1666717