Abstract:In this paper we present our research work: ①We divide 9 connection coefficients into two groups: Group Ainvolving (the linear acceleration)includes Γ001

Γ100

Γ111

Γ122

and Γ133; Group B not involving includes Γ212

Γ233

Γ313

and Γ323. ②Recalling the relation formula: ()R=()Nγ3

where ()R is the linearacceleration in relativistic mechanics

()N the linear acceleration inNewtoneon mechanics

and γ Lorrentz factor. ③Wehave determined that (Γ001)N= -b′b-1

(Γ100)N= -c2b′b-5

(Γ111)N= b′b-1

(Γ122)N=-rb-2

(Γ133)N= -rb-2sin2θ. ④We havedetermined that (Γ001)R = (-b′b-1)γ3

(Γ100)R = (-c2b′b-5)γ3

(Γ111)R = (b′b-1)γ3

(Γ122)R = (-rb-2)γ3

(Γ133)R = (-rb-2sin2θ)γ3. ⑤Wehave proved that Γ001=A′/(2A)=-b′b-1

Γ100 = A′/(2B) = -c2b′b-5

Γ111 = B′/(2B)= b′b-1

Γ122 = -rB-1 = -rb-2

Γ133 = -rB-1sin2θ= -rb-2sin2θ. (6)We havedetermined that (Γ112)NR = r-1

(Γ233)NR = sinθcosθ

(Γ313)NR= r-1

(Γ323)NR = cotθ.⑥We have analyzed Schwarzschild solution

anddrawn two conclusions: (a)B=(1-2GM/(c2r))-1 = (1-r2/c2)-1 =γ2

indicating that it involves Newtoneon formula of energy conservation. (b)Inthe case of the weak gravitational field

GM/(c2r)1

B = (1-2GM/(c2r))-1 ≈ 1 +2GM/(c2r) ≈ 1 + 2GM/(c2r) + (GM/(c2r))2 = (1+GM/(c2r))2 = γ2

therefore

γ= 1 +GM/(c2r) = b

it holds too

in the case of the strong gravitational field.(8)Substituting the needed expressions into equations

and applying therelation formulas

we can simplify the equations

Obtaining the relativisticsolution:-c2dτ2 = c2(1+GM/(c2r))-2dt2 - (1+GM/(c2r))2dr2-r2dθ2-r2sin2θdφ2