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

Ozean Journal of Applied Sciences 1(1), 200833)(1,)(1,,2233322222111000 xfgxfgfgfg−= −−= −= −=Also, the reciprocal metric tensors are given as,)(11,)(1,1,12233322222111000xfgfxgfgfg−= −−= −= −=Now we get the non-zero components of Christofell symbols of 2 nd Kind,⎟⎠⎞∂∂−∂∂+⎜⎝⎛∂∂=Γkkkkxgxgxgg010110000121100001121xff∂∂=Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg000000110021101100121xff ∂∂=Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg111111111121111111121xff ∂∂= −Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg222222112221( )2212112211121xxff−∂∂= −Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg212112222121)(11)(12121222221xxffx−∂∂−=Γ122221121xff∂∂=Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg222222222221222222222211121fxxfx⎟⎟⎠⎞⎜⎜⎝⎛−∂∂−=Γ)(1222222xx−= −Γ∴⎟⎠⎞⎜⎝⎛∂∂−∂∂+∂∂=Γkkkkxgxgxgg333333223321