Browsing by Author "De Silva, Nalin."

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    A metric which represents a sphere of constant uniform density comprising electrically counterpoised dust,
    (Faculty of Graduate Studies, University of Kelaniya, 2008) Wimaladharma, N.A.S.N.; De Silva, Nalin.
    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 .!!! = 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) 154 Proceedi11gs of the A1111Ua/ Research Symposium 2008- Faculty of Graduate Studies U11iversity of Kela11iya 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 ))