- In This Context What Does Affine Parameter Mean Does It Represent Time Spatial Coordinates 1 (82.24 KiB) Viewed 12 times
In this context, what does "affine" parameter mean? does it represent time, spatial coordinates?
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In this context, what does "affine" parameter mean? does it represent time, spatial coordinates?
In this context, what does "affine" parameter mean?does it represent time, spatial coordinates?
uv To proceed further, we must calculate the connection coefficients lº corre- sponding to our static isotropic metric. This can be done in two ways. The quicker route (with any metric) is to use the Lagrangian procedure for geodesics discussed in Section 3.19. This involves writing down the 'Lagrangian' L = 8µvx¹x¹, in which i denotes dx/do, where o is some affine parameter along the geodesic. Subtituting L into the Euler-Lagrange equations then yields the equa- tions of an affinely parameterised geodesic, from which the connection coeffi- cients can be identified. Since later we will discuss the motion of particles in the
uv To proceed further, we must calculate the connection coefficients lº corre- sponding to our static isotropic metric. This can be done in two ways. The quicker route (with any metric) is to use the Lagrangian procedure for geodesics discussed in Section 3.19. This involves writing down the 'Lagrangian' L = 8µvx¹x¹, in which i denotes dx/do, where o is some affine parameter along the geodesic. Subtituting L into the Euler-Lagrange equations then yields the equa- tions of an affinely parameterised geodesic, from which the connection coeffi- cients can be identified. Since later we will discuss the motion of particles in the