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A metric which represents a sphere of constant uniform density comprising electrically counterpoised dust

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dc.contributor.author Wimaladharma, N.A.S.N.
dc.contributor.author de Silva, N.
dc.date.accessioned 2015-06-01T07:30:35Z
dc.date.available 2015-06-01T07:30:35Z
dc.date.issued 2008
dc.identifier.citation Wimaladharma, N.A.S.N. and de Silva, Nalin, 2008. A metric which represents a sphere of constant uniform density comprising electrically counterpoised dust, Proceedings of the Annual Research Symposium 2008, Faculty of Graduate Studies, University of Kelaniya, pp 154-155. en_US
dc.identifier.uri
dc.identifier.uri http://repository.kln.ac.lk/handle/123456789/7919
dc.description.abstract Following the authors who have worked on this problem such Bonnor et.al 1•2 , Wickramasuriya3 and we write the metric which represents a sphere of constant density p = -1-, with suitable units, as ds2 = 47Z" (e(: ))2 c2 dt2 - ( e(r )Y ( dr2 + r2 dQ 2) ds2 = ( 1 B)' c'dT' - ( D + !)' (dR' + R2dQ') D+-R O��r��a A<R where dQ2 = (dB2 +sin2 BdrjJ2), B(r) is the Emden function satisfying the Emden equation4 with n = 3 . Since the metric has to be Lorentzian at infinity, we can take D = 1 . However, there is an important difference between the above authors and us as they had taken the same coordinate r in both regions, and as a result A = a. In general these coordinates do not need to be the same. In this particular case the coefficients of dQ2 are not of the same form in the above two metrics and that forces us to take two different coordinates rand R. In our approach r=a in the matter-filled region corresponds to R = A in the region without matter. Applying the boundary conditions at r = a or R = A , we have, B1(a )cdt = 1 (I +��) cdT => .!!! = e(a) dT (1+ ��) (i) -2 ( ) -2 ( B (e(a) )3 B' a cdt = ) ( B )3 -7 cdT 1+-A => _dt = _-_B--'(,e(-'-a��-- )Y---=----�(ii) dT A'B'(a{l + ��)' (1+ B => dr A ) -=-dR --B(a) _____ (iii) From (i) and (ii), we have e(a1 = - B (B(a )Y 3 (t+ A) A'll'(a{l+ ��) (1+ B ) From (iv), ( ) = !!_ (vi) Ba A __ (v) Using equation (vi) in equation (v), we have B �� -A'(:: } '(a)�� -a2ll'(a ) . Substituting the value of B in equation (iv), B(a )a = ( 1 + ��) A = A+ B =A- a2B'(a) =>A= aB(a)+ a2B'(a) . Then the metric becomes ds2 = 1 c2 dt2 - (e( )Y (dr2 + r2 dQ2) (e(r )Y r dsz = 1 cz dT z - (1- (a2B '(a))J 2 ( dRz + R z dQ z ) (t _(a'��(a))J' R where A=(ae(a )+ a2B'(a )) en_US
dc.language.iso en en_US
dc.publisher University of Kelaniya en_US
dc.title A metric which represents a sphere of constant uniform density comprising electrically counterpoised dust en_US
dc.type Article en_US


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