[Home] | Introduction to General Relativity. Note « 5 » |
Sm = ∫ L[g]√(-g)dΩ, |
δSm = 1/2 ∫Tabδgab√(-g)dΩ = -1/2 ∫Tabδgab√(-g)dΩ, |
1/2√(-g)Tab = δ√(-g)L/δgab. |
ds2 = r2(dθ2+sin2θ dφ2) |
ds2 = (1-2M/r)dt2-(1+2M/r)(dx2+dy2+dz2) |
Hints: Period=2π/ω, where ω=dφ/dt is the angular frequency which can be found from the geodesic equations Dur=0.
Answer: ω2 = M/r3