Exact Solution Of Einstein's Equation To The Gravitational Field Of ...

Ozean Journal of Applied Sciences 1(1), 200814⎛4 c a ⎞r ⎜1+− ⎟3⎝ 3 r r ⎠This expression, together with the corresponding expansions of f 0 , f 2,f3, satisfies up to the sameaccuracy all the conditions of the problem. Within this expression the condition of continuity does notintroduce anything new, since discontinuous occur spontaneously only in the origin. Then the two constantsa and c appear to remain arbitrary, hence the problem would be physically undetermined. The exactsolution reaches that in reality, by extending the approximation, the discontinuity does not occur at the133origin, but at r = ( a − c)3, and that one must set just c = aFor the discontinuity to go in the origin with the approximation in powers of a and c should survey veryclosely the law of the coefficient in order to recognize the necessity of this link between a and c .CONCLUSIONThis solution is of great importance on account of the fact that it provides a treatment of gravitational fieldsurrounding the sun. To find out the Gravitational field of a mass point we use the Schwarzschild lineelement, the Einstein Law of Gravitation and Ricci theorem in the empty space. Here we get a singularity atr = a , whereas there were two singularities in Schwarzschild another solution. The occurrence of asingularity in the field equation is a draw back of field theory. Einstein attributed this singularity to theelectromagnetic field associated with the interior structure of the particle. He expected to have singularityfree solutions of the field equations of the total field. By total field, we mean a field which is not onlyconcerned with gravitational aspects but it is also concerned with electromagnetic field as well as mesonfield. Thus we may conclude in such a way that the singularity is nothing but the artifact of transformationof coordinates.REFERENCESAtwater, H. A. (1974). Introduction to General Relativity. Pergamon Press, New York, USA.Bergman, P. G. (1942). Introduction to the Theory of Relativity. Perentese Hall, Englewood, New Jersey.Biswas, M. H. A. (2008). Studies on Mathematics and Physics of Collapsing Stars. M. Phil Thesis (notpublished) Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.Biswas, M. H. A., Mallik, U. K., Parvin, S. & Islam, M. A. (2008). Curvature Invariants ofSpherically Symmetric Schwarzschild Solution without Cosmological Constant. Journal ofApplied Sciences Research, 4(1), 16-31.Lawden. D. F. (1968). An Introduction to Tensor Calculus and Relativity. Second edition. Chapmanand Hall Ltd. London.Schwarzschild, K. (1916). On the Gravitational Field of a Mass Point According to Einstein’s Theory.Sitzungsberichte der K¨oniglich Preussischen Akademie der Wissenschaften zu Berlin, Phys.Math. Klasse, 189-196 (Germany).38