Timelike geodesics in Schwarzschild Metric.

  • Thread starter Nilupa
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18
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Please explain me how to derive the Timelike geodesics in Schwarzschild Metric.

Thank you.
 

Bill_K

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To derive the geodesics for any metric, write out and solve the Euler-lagrange equations for the Lagrangian F = gμν(dxμ/ds)(dxν/ds).

For Schwarzschild this is (in the equatorial plane) F = (1-2m/r)-1(dr/ds)2 + r2(dθ/ds)2 - (1-2m/r)(dt/ds)2 . There are three first integrals: one for the t coordinate, one for the θ coordinate, and F itself. The result can be expressed as a differential equation for r(θ).
 
18
0
Thank you so much Bill K.

I derived the equations.
 

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